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Experimental Investigation and Simulation of Split System Air Conditioners Charged
with Zeotropic Refrigerants
T. R. Nygaard and C. O. Pedersen
ACRCTR-72
For additional information:
Air Conditioning and Refrigeration Center University of Illinois Mechanical & Industrial Engineering Dept. 1206 West Green Street Urbana, IL 61801
(217) 333-3115
April 1995
Prepared as part of ACRC Project 29 Experimental Breadboardfor Testing Residential
Air Conditioning Systems Using R-22 Alternatives C. O. Pedersen, Principal Investigator
The Air Conditioning and Refrigeration Center was founded in 1988 with a grant from the estate of Richard W. Kritzer, the founder of Peerless of America Inc. A State of Illinois Technology Challenge Grant helped build the laboratory facilities. The ACRC receives continuing support from the Richard W. Kritzer Endowment and the National Science Foundation. The following organizations have also become sponsors of the Center.
Acustar Division of Chrysler Amana Refrigeration, Inc. Brazeway, Inc. Carrier Corporation Caterpillar, Inc. Delphi Harrison Thennal Systems E. I. du Pont de Nemours & Co. Eaton Corporation Electric Power Research Institute Ford Motor Company Frigidaire Company General Electric Company Lennox International, Inc. Modine Manufacturing Co. Peerless of America, Inc. U. S. Anny CERL U. S. Environmental Protection Agency Whirlpool Corporation
For additional information:
Air Conditioning & Refrigeration Center Mechanical & Industrial Engineering Dept. University of Illinois 1206 West Green Street Urbana IL 61801
2173333115
Experimental Investigation and Simulation of Split System Air Conditioners Charged with Zeotropic Refrigerants
Timothy Robert Nygaard
Department of Mechanical and Industrial Engineering
University of Illinois at Urbana-Champaign, 1995
Abstract
This work evaluates the performance and control of split system air conditioners
charged with a zeotropic, HCFC-22 alternative consisting of HFC-32, HFC-125, and
HFC-134a (23%,25%, and 52% respectively). The study involves the development of
two analysis tools: a split system air conditioner testing facility, and a mathematical system
model that predicts the performance of the facility. The experimentally validated system
model is used to analyze the potential system performance gains resulting from enhanced
evaporator air-refrigerant temperature profiles. In particular, six different evaporator
designs with varying tube arrangements are included in the system simulation to evaluate
the effects of increasing the number of evaporator rows on air conditioner efficiency.
Finally, the control of a system charged with the zeotrope is evaluated. Changes in system
capacity, sensible heat ratio, and system efficiency resulting from controlling evaporator air
flow rate, compressor speed, and expansion valve opening are quantified.
Table of Contents
Chapter Page
L · t f F· . IS 0 Igures •••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• VI
1. Introduction .................................................................... 1
2. Experimental Testing Facility Description ............................ 3 2.1 Refrigerant Loop Component Descriptions ................... 3·
2.1.1 Compressor ..................................................... 3 2.1.2 Compressor Control ........................................... 7 2.1.3 Oil Separator ................................................... 8 2.1.4 Condenser / Receiver / Subcooler ............................ 8 2.1.5 Sampling Valves ••.•••.....•.••.....•....•.....•.......•....•.. 9 2.1.6 Expansion Device .•..•••••...••.....••.•••••.........••........ 9 2.1.7 Evaporator ..................................................... 10
2.2 Evaporator Air Loop Component Descriptions ............. 10 2.2.1 Blower/Blower Control •.•.....•••..•..•........ · .........•••.• 12 2.2.2 Air Flow Rate Nozzle Station ••....•..•••.••.••••..•••..•.... 12 2.2.3 He ate r s .••••.•.....•.••••.•.•.••.....••...••..•....••........•.• 14 2.2.4 Heater Safety Controls .•.••••••••••...•••••....•.•......••..• 14 2.2.5 Humidifier ••...••...........•....••••..••....••••••..•.•.••.... 16 2.2.6 Evaporator Test Section ••...•.••..........•••••..•..........• 18
2.3 System Measurement and Data Acquisition ................... 20 2.3.1 Refrigerant Temperature Measurements ....•....••.......... 20 2.3.2 Refrigerant Pressure Measurements .•.....•.•...••....•..... 20 2.3.3 Refrigerant Flow Meter .••.•.••......•••......•••...•••.•...•• 21 2.3.4 Air Temperature Measurements ••••.•••••..••.•••..•••.•.•... 21 2 . 3 • 5 Air Pressure Measurements .••••..••••..•••......••...•..•••• 21 2.3 .6 Humidity Measurement ..••.••..•••••.••.••••.•••..•.••.•.•.. 22 2.3 . 7 Compressor Power Measurement .•..•••••.•••••.....•.••.... 22 2.3.8 Data Acquisition .•••.•.•••.•••••.•....•.....••••••.••••....... 22 2.3.9 Transducer Calibration Techniques ..•••...•.•.•••........... 23 2.3.10 Gas Chromatograph •.•.•••....••.•....•......•.............•.. 26
3. Mathematical System Model Development ............................ 30
3.1 Model Inputs, Outputs, and Operating Modes ............... 30
3.2 Compressor Model Description .................................. 32 3.2.1 Predicting Refrigerant Mass Flow Rate ..................... 32 3.2.2 Compressor Power Prediction •...•••..•.••.•.....•.•........ 36
3.3 Heat Exchanger Models .. · •......................................... 41 3.3.1 Evaporator Model •..•••.•.•••.••....••....••.....••••...•....• 41 3.3.2 Condenser / Sub cooler Model .••••••••••..•••....•.••...••••. 41
3.4 Pressure Drop Calculations ....................................... 41 3.4.1 Condenser / Subcooler / Liquid Line Pressure
Drop •••••••••••••...•......•.••••.•.•.••••••••••.•••...•.•.••... 42 3.4.2 Expansion Device / Distributor Pressure Drop ...•.•.•••... 43
3.5 Air and Refrigerant. Properties .................................. 46
IV
3.6 ACRC Newton Raphson Solver ......•...•....•.................. 47 3.6.1 EQNS.f ....•.....•.••..................•....•..•.......•....... 47 3.6.2 CHECKMOD.f ••••.••...•..•...••••..••.•.....••.••••••...••.. 48 3.6.3 3.6.4 3.6.5 3.6.6 3.6.7
EQ UIVLNT .IN C ...•...........•.....•.....•.......•...•...••. 48 X K ••••••••••••••••••••••••••••••••••••••••••••••••••.•••••..••. 48 I:NITMOD.f ••••••••••••••••••••••••••••••.•••.••••••••..••••••• 49 SL VERSET ••••••••••••.•••••.•...••••••••••.••....••••••.•.••. 49 INSTR .••••...•••.................................•............ 50
3. 7 System Model Validation ..•.• · ...................................... 51
4. System Performance and Control Analysis ...•..•.•.................. 57 4.1 Effect of Evaporator Design on System
Performance •••••..••..•..•.......•.....••......••....•..••........... 57
4.2 System 4.2.1 4.2.2
Control Analysis .......................................... 62 Valve Position and Evaporator Air Flow Rate Control ••.• 62 Compressor Speed and Evaporator Air Flow Rate Con trol ..•••.....••..•••••..•.•••...........•......•...•....•.•. 71
5. Project Summary and Conclusions .•...••..............•..............•. 79
List of References ............................................................... 81
A ppendix A: Wiring Schematics .......••.........•..•...................... 83
Appendix B: Data Acquisition Terminal Panel Connections ••.•.•.. 86
Appendix C: Facility Facility
Facility Operation ............................................ 90
Startup Instructions ...............•........................... 90
Shutdown Instructions .•.....•.•.....•..•...•.......•......... 93
Appendix D: Inverter Output Power Measurement Uncertainty ••. 94
Hard ware ...............••...••..•..............•...................•........ 94 Current Measurement ..................... ~ ••••••••••..•••.....•••..... 94 Voltage Measurement ••••.....•..• ~ .....••.•.•••••••..••••...•........ 95
Experimental Method ...•................................................ 95
Itesults ....................................................................... 97
Appendix E: List of Component Manufacturers ........••...•••...•••. 101
Appendix F: Selected System Model Source Code •..•.............••. 102
E~NS.f •.•••.•••..•...•••.•.•••••••..•...•.•..•.•..•.•.••.....••••.•..•.•... 102 <:HECI(MOI>.f .........•.........••...••.•.••••.•..•.••......••........... 108
E~UIVLNT.IN<: ...••...••••...••...•..••......•.•....•..........•....... 110 "I( ..••..•..••..•....•....••.•.....•..•......•.•....••••...•.......•.....•... 111
INITMOD.f ..••....••........••.•.•....•.•..••.•.....•...•.•.....•....•.... 112
SLVEItSET •••..•.....••..•••••..••••.•.••.•.•••..••..•..••.••...•...•.•••. 115
v
List of Figures
Figure Page
2.1 Air Conditioner Testing Facility Schematic .• ~ •..•.•.•.•••.........••.... 4
2.2 Refrigerant Loop Schematic ..•••••••.••.••...• eo ••••••••••••••••••••••••••• 5
2.3 Illustration of Split System Condensing Unit ..•.••.........•........•... 6
2.4 Condenser/ReceiverlSubcooler Flow Schematic ...........••..••....••.. 9
2.5 Evaporator Coil Circuitry ••••..•.....•.•...••.•.••.....••.•..•••........•. 10
2.6 Air Loop Schematic .•....••..••..••••......•..•.•......•......•..••...•••. 11
2.7 Air Flow Rate Measurement Station .•...............•......•......••.... 13
2.8 Air Heating Section •••••.••.••••. ' .•..•••••. __ •••••••••••••.•••...••.•.•...• 15
2.9 Facility Humidifier (background) and Preheater (foreground) •.•••••.......•••••...•.•••••..•..••••..••.........••.•....•••. 16
2.10 Evaporator Test Section ........................•.......................... 18
2.11 Refrigerant Pressure Transducer Calibration •••.•.....•..........••.•••• 24
2.12 Air Pressure Transducer Calibration ...•.....•..••....••....••.......•••• 25
2.13 Thermocouple Calibration" ...•••..•.•.•.•.•...•.•..............•.....•.•.• 26
2.14 Example Integrator Output •..••••......•..•••••••.•••...•.••.......•••••.• 29
3.1 Compressor Model Diagram ..•.•••••............•••....•.....•••...•...•• 32
3.2 Volumetric Efficiency vs. Compressor Speed & Pressure Ratio •••••••.•••••.•..••..••.•••..•••...•••••••••••••••.••.•.•..•...••..•••.. 34
3.3 Volumetric Efficiency Prediction Accuracy ••.•••••••••••••.•.••.••.•••• 35
3.4 Inverter Efficiency vs. Compressor Speed ....•.•....•......••.......••• 38
3.5 Isentropic Work Efficiency vs. Compressor Speed and Pressure Ratio .•.•..••...•••.•••••••••.....••...•............•.••.......... 39
3.6 Isentropic Work Efficiency Prediction Accuracy ••••••.••••••••..•.•..• 40
VI
3.7 Condenser I Subcooler I Liquid Line Pressure Drop Agreement ..................................................... .............. 44
3.8 Expansion Device Pressure Drop Agreement ..•...•..•.•.•.•...•..••.... 46
3.9 Refrigerant Mass Flow Rate Comparison .....••....•.•...••.......•••... 52
3.10 Evaporator Capacity Comparison ........................................ 53
3.11 Evaporator Pressure Comparison .......••..•••.•.............•.....•.•.• 54
3.12 Compressor Power Comparison .......................................... 55
3.13 COP Comparison .......................................................... 56
4.1 Circuitries of Cross· Counterflow Evaporator Coils ..•••.••..•..•...•.. 58
4.2 Effects of Varying Tube Arrangement on Compressor Power and Air Pumping Power using Zeotropic Mixture of HFC· 32, HFC·125, HFC·134a (23%, 25%, 52%) .•.••....•..•••.•...•..•••. 60
4.3 Effects of Varying Tube Arrangement on System COP using Zeotropic Mixture of HFC·32, HFC·125, HFC·134a ..••.......•....• 61
4.4 Effects of Varying Tube Arrangement on System COP using HCFC·22 ................................................................... 61
4.5 Total and Latent Capacity Resulting from Varying Expansion Valve Position and Evaporator Air Flow Rate ••.••.••..•.•...•••.•..... 64
4.6 Evaporator Superheat Resulting from Varying Expansion Valve Position and Evaporator Air Flow Rate ..••.•..••....••...•..•... 65
4.7 Sensible Heat Ratio Resulting from Varying Expansion Valve Position and Evaporator Air Flow Rate ..•.•....•..•.•..•...••.•. 66
4.8 Compressor and Air Pumping Power Resulting from Varying Expansion Valve Position and Evaporator Air Flow Rate .........•.••• 67
4.9 System COP Resulting from Varying Expansion Valve Position and Evaporator Air Flow Rate ••.....••••.......•.•....•...•.•.• 68
4.10 Relative Magnitude of Effective Cycling Efficiencies .•••••..••..••.... 71
4.11 Total and Latent Capacity Resulting from Varying Compressor Speed and Evaporator Air Flow Rate •••••••••.......••.•.. 74
4.12 Sensible Heat Ratio Resulting from Varying Compressor Speed and Evaporator Air Flow Rate .................................... 75
4.13 Evaporator Pressure Resulting from Varying Compressor Speed and Evaporator Air Flow Rate ••••••.•••••••••••••.•....•••..•.... 76
vii
4.14 Compressor and Air Pumping Power Resulting from Varying Compressor Speed and Evaporator Air Flow Rate •.•......•.......••... 77
4.15 System COP Resulting from Varying Compressor Speed and Evaporator Air Flow Rate ................................................. 78
A.I Compre$so"r Control Schematic ........................................... 84
A • 2 Heater Control Schematic ................................................. 85
C.l Experimental Facility Control PaneL .••..••..••.••.................•..•. 91
D.l Variable Speed Drive Voltage I Current Conditioning Circuitry ..................................................................... 96
D.2 Variable Speed Drive Output Voltage, Current, and Phase Angle at 41.2 Hz .......................................................... 98
D.3 Variable Speed Drive Output Voltage, Current, and Phase Angle at 47.5 Hz .......................................................... 99
D.4 Variable Speed Drive Output Voltage, Current, and Phase Angle at 60.0 Hz ......................................................... 1 00
viii
Chapter 1
Introduction
The ozone layer is a reservoir of ozone molecules located in the stratosphere
approximately 25 to 30 km above sea level. It is responsible for protecting the earth from
the harmful effects of solar radiation. In recent years, concerns have surfaced regarding the
depletion of the ozone layer caused by its interaction with commonly used refrigerants.
The refrigerants that have generated the most concern from an ozone depletion
standpoint are known as CFCs (chlorofluorocarbons). Although CFCs are stable near the
earth's surface, they dissociate when they enter the stratosphere due to decreased protection
from high energy ultraviolet photons. The resulting free Chlorine atoms react with ozone
molecules to deplete the ozone layer.
This study focuses on evaluating a replacement for HCFC-22, a primary refrigerant
used in air conditioning applications. HCFC-22 is a hydrochlorofluorocarbon whose
ozone depletion potential is much lower than that of CFCs. While HCFCs contain
potentially harmful Chlorine atoms, their hydrogen component increases their susceptibility
to destruction within the troposphere. Therefore, statistically very few HCFC molecules
survive to release Chlorine into the stratosphere. The ozone depletion potential for HCFCs
is typically only 2 to 10 percent of the ozone depleuon potential for CFCs. [1]
Despite the relatively low ozone depletion potential of HCFC-22, efforts are under
way to develop ozone safe replacements for the refrigerant. One proposed class of
replacements are known as zeotropic mixtures. These replacements have the potential to
improve air conditioning cycle efficiency due to the temperature glide that they experience
during an isobaric phase change. This temperature glide could improve the matching
between temperature profiles of the refrigerant and the external fluid in the heat exchangers,
thereby reducing the heat transfer irreversibilities and improving system performance.
The primary emphasis of this work is to evaluate the performance and control of
split system air conditioners using a zeotropic HCFC-22 alternative consisting of HFC-32,
HFC-125, and HFC-134a (23%, 25%, and 52% respectively). The study involves the
completion of four major objectives. These include:
1
• the construction of an instrumented, 3 ton, split system air conditioner testing
facility with complete system loading and operating control
• the development and validation of a complete system simulation that accurately
represents the above facility
• analysis of the potential performance gains associated with enhanced evaporator
temperature glide matching
• investigation of the effects of operating parameters such as air flow rate on
system performance and control
2
Chapter 2
Experimental Testing Facility Description
A 3 ton split system testing facility has been constructed to evaluate air conditioner
performance using zeotropic refrigerants. The facility is highly flexible, providing the
operator with complete control of evaporator loading conditions. A central control center
provides easy adjustment of evaporator air inlet flow rate, temperature, and humidity. In
addition, the system capacity and refrigerant operating temperatures are easily tunable.
The experimental testing facility is comprised of four main parts: a 3 ton split
system refrigerant loop, an evaporator air loop with temperature and humidity control
capabilities, system measurement and data acquisition equipment, and a gas
chromatograph. The system is shown schematically in Figure 2.1. A complete description
of each of the main components follows.
2.1 Refrigerant Loop Component Descriptions
With the exception of an oil separator and a water cooled condenser / subcooler, the
refrigerant loop contains standard components found in most air conditioning systems.
Figure 2.2 shows the schematic. layout of the refrigerant loop. In addition, a labeled
illustration showing the actual appearance of the facility condensing unit is provided in
Figure 2.3. Detailed descriptions of each of the main components appear in the following
paragraphs.
2.1.1 Compressor
A hermetic reciprocating compressor is used in the facility. Its nominal ratings are
included in Table 2.1.
3
Compressor Polyol-ester oil Inv~'rT".r-n!rlVI~n
Receiver
Sub-cooler Water-cooled
-
Blower Inverter-driven
Flowmeter
Coriolis based
Gas Chromatograph Evaluate blend composition
Data Acquisition
ozzle Station Air flow
".,:.,t'Trlll' Heaters Air temperature control
SYMBOLS [!] Air Temperature []] Air Humidity ~ Air Pressure Drop
Refrigerant Pressure Refrigerant Temperature Refrigerant Pressure Drop Refrigerant Flow Rate Compressor Power Input
Refrigerant Sampling Station
Figure 2.1: Air Conditioner Testing Facility Schematic
4
To Drain
Water Condenser
From~:;:::~""'--1C:====:::::J====~ Supply
Flowmeter
Expansion Valve
Ball
High and Low Pressure lines
Sub-cooler
=-Figure 2.2: Refrigerant Loop Schematic
5
1 Hermetic Compressor
2 Oil Separator
3 Condenser Pressure Gage
4 Mechanical Condenser Pressure Controller
5 Subcooler Water Pressure Regulator
6 Subcooler Water Control Needle Valve
7 Coaxial Condenser
8 Coaxial Subcooler
9 Refrigerant Sampling Ports
Figure 2.3: Illustration of Split System Condensing Unit
6
Table 2.1: Nominal Compressor Specifications
Input Voltage 200/230 Volts @ 60 Hz - 3 Phase
Rated Load Current 9.6 Amps
Rated Power 3170 Watts
System Capacity 32,500 BtuIhr (9520 Watts)
Total Displacement 3.70 inl\3/rev (6.06E-5 mI\3/rev)
The compressor was charged at the factory with mineral oil usually used for
R221R502 systems. Since mineral oil is immiscible in the R22 replacement blend used in
this study, the compressor was drained, flushed and recharged with Mobil Arctic 32, a
polyolester alternative.
2.1.2 Compressor Control
A compressor control scheme similar to that found in refrigeration applications is
implemented in the testing facility. The compressor starts automatically when the
compressor suction pressure exceeds approximately 20 psig. A solenoid valve in the liquid
line provides on/off control of the system. When the valve is closed, the compressor
pumps refrigerant out of the evaporator until the compressor suction pres rre drops below
the 20 psig threshold. At that time, a pressure switch connected to the low pressure side of
the system disables the compressor. When the liquid line solenoid valve is reopened,
refrigerant flows into the evaporator causing the suction pressure to increase. The
compressor starts when the low suction pressure threshold is exceeded.
The purpose of this type of compressor control in refrigeration applications is to
protect the compressor from damage by preventing liquid refrigerant from entering the
compressor at low ambient temperatures during startup. In this case, however, the control
scheme holds the evaporator pressure at values within the active range of the evaporator
pressure transducers while the unit is shut down. In addition, the control scheme facilitates
the removal of evaporators from the test section by removing the majority of the refrigerant
charge from the low pressure side.
A normally closed discharge pressure switch is wired in series with the suction
pressure. cutout switch described above. It disables the compressor in the event of an
abnormally high condensing pressure.
7
Additional information about the compressor control implementation is shown on
the "Compressor Control Schematic" in Appendix A.
2.1.3 Oil Sepan"tor
Upon exiting the compressor, the refrigerant enters an oil separator which removes
the oil, and makes the heat transfer processes and thermodynamic properties more
predictable throughout the rest of the system. The oil I refrigerant mixture flows through a
borosilicate coalescent filter. The oil collects on the filter and drips into the separator
reservoir. A float valve in the reservoir regulates the flow of oil back to the low pressure
side of the compressor. The separator operates with approximately 14 ounces of oil in its
reservoir. The manufacturer claims that it recovers 99.9% of the oil from the compressor
discharge refrigerant.
2.1.4 Condenser I Receiver I Sub cooler
A water cooled, coaxial, counterflow heat exchanger is used as the testing facility
condenser. A mechanical controller governs the heat exchanger water flow rate to maintain
a preset condensing pressure.
A receiver located immediately after the condenser is partially filled with liquid
refrigerant for all operating conditions ensuring saturated liquid exit conditions during
steady state operation.
A second coaxial, counterflow heat exchanger subcools the refrigerant to guarantee
liquid flow through the refrigerant mass flow meter. A water pressure regulator prevents
water supply pressure changes from causing variations in the amount of subcooling over
time. The subcooler water flow rate is adjusted with a needle valve. See Figure 2.4 for a
schematic of the condenser I receiver I subcooler arrangement and Figure 2.3 for an actual
illustration of the condenser, subcooler, and water controls.
8
Water Source
P refrigerant comp discharge
Refrigerant Flow
condenser
Pressure Regulator
Needle Valve
Figure 2.4: CondenserlReceiverlSubcooler Flow Schematic
2.1.5 Sampling Valves
. .
Water Drain
Two sampling valves for extracting single phase refrigerant samples are shown in
Figure 2.3. Vapor samples are taken from the compressor discharge line. Liquid samples
are extracted from the liquid line following the subcooler. A gas chromatograph is used to
analyze the samples and determine the refrigerant composition in the system.
2.1.6 Expansion Device
The expansion device used on the testing facility is a manually adjustable, 20 tum
needle valve. A micrometer vernier handle allows for precise valve position indication and
repeatability .
9
2.1.7 Evaporator
The test facility evaporator is a standard, crossflow, air-refrigerant heat exchanger.
Four horizontal rows ot'copper refrigerant tubing spaced 1.5 inches (3.8 cm) apart make
up two equivalent flow circuits - one above the other. Figure 2.5 illustrates one of the
equivalent circuits. Nine aluminum rippled fins per inch run vertically across the·
refrigerant tubing. The frontal area of the heat exchanger is 4.0ftA2 (0.37 mA2)
z (into page)
ytL x
Coil face area in the y-z plane: 24x24 in
NOTE: Refrigerant leaving inlet manifold is split in half. Only the top half of the cvJ is shown in this schematic
Figure 2.5: Evaporator Coil Circuitry
AirFlow
SYMBOLS
@ Flow out of the page
To outlet ~ Flow into the page manifold
...-U-bend
2.2 Evaporator Air Loop Component Descriptions
The evaporator air loop contains the necessary components to provide temperature
and humidity conditioned air for realistic loading of the cooling coil. Figure 2.6 shows the
layout of the air loop, and each of the primary components is described in the following
paragraphs.
10
--
)
G>
t Air Humidifier
BLENDER
5.8 kW SCR Controlled Trim Heater
Figure 2.6: Air Loop Schematic
5.5 kW Baseline Heater
Refrigerant Li
Compressor Unit
Blower
2.2.1 BlowerlBlower Control
Variable air flow rates are provided by a variable speed, 7.5 HP (5.6 kW) radial
blade blower. A variable frequency drive provides adjustable blower speeds for air flow
rates ranging up to 1750 CFM (830 LIs).
2.2.2 Air Flow Rate Nozzle Station
Air flow rate is measured according to the recommendations of ANSI! ASHRAE
41.2-1987 [2]. A 42 inch by 36 inch (1.07 by 0.91 m) section of duct contains a
permanently mounted, 6 inch (15.2 cm) diameter nozzle. In addition, a position is
provided for a second nozzle. The operator can easily install either a 2.7 inch (6.9 cm) or
5.5 inch (14.0 cm) diameter nozzle in this second position depending upon the desired air
flow rate range. In addition, plugs are provided for each of the nozzles in the event that
only one nozzle is desired. Table 2.2 provides the alr flow rate ranges for each nozzle
configuration.
Table 2.2 Nozzle Configuration Selection
Nozzle Configuration Air Flow Rate Range
5.5 inch (14.0 cm) 300-1100 CFM (140-520 Lis)
6.0 inch (15.2 cm) 500-1300 CFM (240-610 Lis)
6.0 inch (15.2 cm)+ 2.7 inch (6.9 cm) 600-1600 CFM(280-760 LIs)
6.0 inch (15.2 cm) + 5.5 inch (14.0 cm) 800-1750 CFM (380-830 LIs)
12
5 thermocouple grid (to calculate air density)
Atm.
Figure 2.7: Air Flow Rate Measurement Station
Measurements are taken from the nozzle station as shown in Figure 2.7. The air flow rate
is then calculated using the following relationships:
Q=1096.7·Y }~P ...... :~C A exp p £... D.l 1
air i=1
(2.1)
Yexp =1.0-0.548·(1.0-a) (2.2)
a = 1.0 _ 0.0360875· AI> nozzle
P nozzle in
(2.3)
CD.i = 1. 0 - (0.10276 * ReJMI4 (2.4)
(2.5)
13
where:
Q == Air Flow Rate (CFM)
Yexp == Expansion Factor
ex == Alpha~Ratio
M' nozzle == Differential Pressure Across Nozzles [in H20]
P nozzle in == Nozzle Inlet Pressure [psi]
Pair == Air Density [lbmlft3]
CD,i == Discharge Coefficient for Nozzle i
Rei == Approximate Reynolds Number for Nozzle i
2.2.3 lIeaters
Two electric resistance heaters are used to adjust the temperature of the air entering
the evaporator test section as shown in Figure 2.8. One of the heaters is SCR regulated,
and provides up to 5.8 kW of power to the air stream. A PID controller provides accurate,
closed loop regulation of the evaporator air inlet temperature. The controller reads air
temperature at the evaporator inlet using a T-type thermocouple and provides a 4-20 rnA
SCR control signal. In cases where the 5.8 kW output of the controlled heater is
ir nufficient, the second heater can be used. This heater is not SCR regulated. It simply
provides 5.5 kW of baseline power to the air stream. When used in conjunction with the
SCR controlled heater, air stream input power is regulated between 5.5 and 11.3 kW.
2.2.4 lIeater Safety Controls
Failsafe mechanical controls are implemen'ted in the testing facility to prevent the
possibility of overheating. Suppose, for instance, that the belts failed on the blower
causing the air flow to cease. Without heater safety controls, the heaters would remain
enabled causing an overtemperature condition.
In order to prevent such an occurrence, an air flow proving switch is implemented
in the heater control circuitry as shown in Figure 2.8. The device detects the stagnation
pressure in the duct using a pitot tube arrangement. The heaters are physically disabled
when the stagnation pressure in the duct approaches atmospheric pressure.
14
Air Flow
-------------------------------------On/Off Switch
~--~~------------~~~:~~~~~~~~~
PIO Controller
Air Flow Sensor
Figure 2.8: Air Heat .... ig Section
-------------------------------------
3 phase, 240V open element
slip-in heater
5.5 kW
4 space heaters
o kWto 5.8 kW
In addition to the air proving switch, high temperature cutouts prevent overheating
due to a refrigeration system or heater controller failure. A user-adjustable high
temperature cutout is mounted downstream of the heating section. It physically disables
both heaters when the air stream temperature exceeds the preset threshold temperature. A
redundant overtemperature switch will disable the baseline heater if the temperature in its
vicinity exceeds 130-140 of (55-60 °C).
For additional detail regarding the implementation of the heater safety controls, see
the "Heater Control Schematic" in Appendix A.
15
2.2.5 Humidifier
Air humidity control is provided by an 8.5 kW, stainless steel boiler mounted on
the wall near the ductwork as shown in Figure 2.9. The boiler chamber is filled with
water, and an electric resistance heating element submerged in the water provides the
necessary heat input to produce up to 25.5lbslhr (3.21 g/s) of steam. The steam leaves the
top of the boiler chamber and enters the air duct through a 9 foot (2.7 m) section of 1.5
inch (3.8 cm) I.D. high temperature hose. A stainless steel distnbutor mounted within the
duct evenly disperses the vapor into the air stream.
Figure 2.9: Facility Humidifier (background) and Preheater (foreground)
16
Humidifier Water Level Control
The water level in the boiler is controlled electronically. The boiler chamber holds
approximately 7.0 gallons (27 L) of water when full. After approximately 1.0 gallon (3~8
L) of water is removed as steam (about 6 gallons or 23 L remain), the controller opens a
solenoid valve allowing supply water to refill the chamber.
Humidity Control
Evaporator air inlet dew point is controlled to within +/- 0.4 of (+/- 0.2 °C) using a
PID controller. A chilled mirror dew point sensor samples air from the evaporator inlet and
provides feedback for closed loop dew point control. The PID controller provides a 4-20
rnA control signal for an SCR controller which regulates the humidifier power. An air flow
proving switch mounted in the duct disables the humidifier if air flow ceases due to a
blower failure.
Humidity Control Limitations
The humidifier does an excellent job of providing a constant supply of water vapor
to the air stream as long as the electronic fill cycle is not enabled. During the fill cycle,
however, a significant portion of the energy dissipated in the heating element is used to heat
up the incoming water rather than to produce desired water vapor. This results in a
noticeable decrease in the amount of vapor supplied to the air stream. This is not a concern
when the humidifier load is low since refills are infrequent. However, as the
humidification load increases, it becomes difficult or impossible to collect system data due
to significant decreases in the time available between boiler refills.
Two steps were taken to decrease the effect of the refill cycle on humidifier
performance. First, a standpipe was obtained from the humidifier manufacturer and
installed in the boiler chamber. The standpipe is simply a tubing assembly which forces the
incoming water to the bottom of the humidifier during the refill cycle. Since the incoming
water is cooler and has a greater density than the water in the humidifier, it will tend to
remain at the bottom of the chamber. By protecting the interface between the liquid and the
17
vapor in the boiler chamber, the standpipe improves humidifier performance during the
refill cycle. Secondly, a small hot water heater shown in the foreground of Figure 2.9 was
installed to preheat the supply water before it enters the humidifier. This greatly decreases
the amount of time and energy required to heat the incoming water to its boiling
temperature. As a result, the humidifier recovers from a refill cycle much more quickly.
2.2.6 Evaporator Test Section
The evaporator test section houses all of the necessary components for measuring
the air side performance of an evaporator coil. It consists of 6.0 feet (1.8 m) of insulated,
36 inch by 30 inch (0.91 by 0.76 m) ductwork. The test section is divided into four,
separable parts as shown in Figure 2.10: the inlet air measurement section, the evaporator
.section, the outlet air measurement section, and the mixed outlet air measurement section.
Descriptions of each of these four sections follow.
Humidity Sampler
7 thermocouple 9 thermocouple
" grid
~
Air Flow
IScreen I
Figure 2.10: Evaporator Test Section
18
grid
1"\
t Evaporator Coil
I Blender
Humidity Sampler
I
Inlet Air Measurement Section
Evaporator air inlet temperature and humidity are determined in the inlet air
measurement section. This 20 inch (0.51 m) long segment houses a 7 thermocouple grid
for accurate air inlet:temperature measurements, a single thermocouple for temperature
control feedback, and an air sampler which provides a small flow of air that passes through
the evaporator inlet dew point transducer. The air sampler is made of a section of copper ..
tubing that spans the entire width of the duct to provide an average air sample for humidity
measurement. A screen located on the upstream side of the inlet air measurement section
improves the uniformity of the air velocity across the test section.
Evaporator Section
In addition to housing the coil, the 20 inch (0.51 m) long evaporator section is
equipped with a drip pan for catching any condensate that forms on the evaporator. The
condensate water drains through a fitting in the ductwork, and is carried away through
PVC piping to a building drain. Sixteen thermocouples soldered to the return bends on the
evaporator measure the refrigerant temperature variation as it passes through the coil.
Outlet Air Measurement Section
Immediately after passing through the evaporator coil, the air enters the 15 inch
(0.38 m) long outlet air measurement section. A thermocouple grid provides nine
individual temperature measurements across the face of the coil. Since the air in the outlet
air measurement section has not been forcibly mixed, a quantitative view of temperature
stratification at the coil exit can be obtained. The nine thermocouple readings can also be
averaged for air/refrigerant heat balance calculations.
Mixed Outlet Air Measurement Section
The upstream side of the 15 inch (0.38 m) mixed outlet air measurement section
contains an air blender which improves the uniformity of the air humidity. An air sampler
19
similar to that found in the inlet air measurement section spans the entire duct, and provides
air flow through a dew point transducer.
2.3 System Measurement and Data Acquisition
The experimental testing facility is heavily instrumented. In all, 54 system
measurements are recorded during data collection. These include 19 air temperatures, 21
refrigerant temperatures, 6 refrigerant pressures, 4 air pressures, 2 dew points, compressor
input power, and refrigerant flow rate. The following is a description of the transducers
and data acquisition equipment used for data collection in this study. Also included, are the
methods used to calibrate the equipment.
2.3.1 Refrigerant Temperature Measurements
Refrigerant temperatures are measured using 30 gauge copper-constantan (T type)
thermocouples. Important temperatures are measured using thermocouples located directly
in the flow. Less critical measurements are made with soldered and insulated surface
thermocouples. All thermocouple wire was manufactured with special limits of error for
improved measurement accuracy.
2.3.2 Refrigerant Pressure Measurements
Refrigerant loop pressures are measured using variable capacitance pressure
transducers. As the refrigerant pressure changes, a diaphragm in the transducer moves
relative to an insulated electrode plate. The change in capacitance of the sensor is a function
of the refrigerant pressure change. The transducers produce a 0.1 to 5.1 Volt signal that is
proportional to pressure. According to the manufacturer's specifications, accuracies of
0.13% of the full scale pressure range are expected from gage pressure transducers, and
accuracies of 0.21 % of the range are expected from differential pressure transducers.
20
2.3.3 Refrigerant Flow Meter
A coriolis based. flow meter measures system refrigerant flow rate. Its accuracy is
independent of fluid physical properties and flow profiles. The flow meter contains a V
shaped flow sensor which is vibrated at its natural frequency. The coriolis acceleration of
'the refrigerant flowing into the sensor produces a force perpendicular to the direction of
refrigerant flow on the inlet side of the V-tube. The coriolis acceleration of the refrigerant
flowing out of the sensor produces a force of the same magnitude but opposite direction on
the outlet side of the V-tube., The forces form a couple which tries to twist the V-tube.
The flow rate, then, is proportional to the amount of torque applied to the V-tube sensor.
The manufacturer claims flow measurement accuracy of +/- 0.2% of flow rate and +/-
0.005Ib/min (+/- 0.002 kg/min) zero stability.
2.3.4 Air Temperature Measurements
Shielded, 30 gauge, copper-constantan thermocouple pairs are used for all air
temperature measurements. The thermocouple wire was manufactured with special limits
of error for improved measurement accuracy. The thermocouples are suspended in the air
stream by string which forms a grid in the duct section.
2.3.5 Air Pressure Measurements
Variable capacitance air pressure transducers measure static pressures in the facility
air loop. The air pressure applied to the transducer determines the position of a stainless
steel diaphragm relative to an electrode. Positive pressure moves the diaphragm closer to
the electrode while negative pressure pulls it away from the electrode. The capacitance
between the diaphragm and the electrode is detected and converted to a linear, 0 to 5 Volt
signal. The manufacturer promises an accuracy of +/- 1 % of full scale for the 0 to 2.5 in
H20 (0 to 623 Pa) and 0 to 5 in H20 (0 to 1245 Pa) transducers used in this study.
21
2.3.6 Humidity Measurement
The water vapor content in the air stream is measured both before and after the .,
evaporator using optical condensation hygrometry. The device used to perform this
technique is known as a chilled mirror dew point sensor. A small sample of system air is
routed past a metallic mirror surface in the sensor. This surface is cooled using a
thermoelectric heat pump until condensation begins to form. The condensation is detected
optically, and the heat pump cooling rate is controlled to provide a mirror temperature at or
very near the transition (dew point) temperature. A platinum resistance thermometer
accurately measures the temperature near the mirror surface. In additional to a direct
numerical display of dew point temperature, the transducer provides analog and digital dew
point outputs for use with a data acquisition system or humidity controller.
Since optical condensation hygrometry is extremely accurate, chilled mirror dew
point measurement devices are widely used as a standard for humidity measurement. The
dew point sensors on the testing facility provide accuracies of +/- 0.4 OF (+/- 0.2 °C).
2.3.7 Compressor Power Measurement
Compressor power is measured at the input to the variable speed compressor drive
using a three-phase, AC watt transducer. The accuracy of the transducer ~~ +/- 0.2% of the
power reading, and is independent of variations in voltage, current, power factor, or load.
The transducer supplies a 0 to 5 Volt signal proportional to the compressor power, and has
a full scale range of 0 to 8 kW.
2.3.8 Data Acquisition
A user-friendly data acquisition system operating in a PC environment is used for
collecting system data. An easy to understand operator interface provides valuable
capabilities such as time averaging, plotting, and mathematical manipulation. In addition,
the data acquisition system provides on-line screen outputs for continuous monitoring of
facility measurements and the ability to log data in an organized fashion to a text file for
future analysis.
22
The data acquisition hardware consists of two parts: data acquisition cards and
terminal panels. The data acquisition cards reside within the personal computer and
perfonn the necessary analog to digital conversion of transducer signals. The cards are
available with either 8 or 16 differential analog inputs and provide 9 to 16 bit resolution.
The terminal panels are mounted away from the computer and provide termination points
for the transducer signal wiring. The panels also provide cold junction compensation for
thermocouple measurements. Despite this capability, the experimental test facility uses an
ice bath temperature reference for increased temperature measurement confidence. See
Appendix B for a detailed layout of the terminal panel connections.
2.3.9 Transducer Calibration Techniques
All experimental data taken from the facility are recorded by the data acquisition
system in raw fonn. In other words, the actual voltage readings from the thennocouples
and transducers are written to the data files. Calibration curves are used after the data is
recorded to determine the pressures, temperatures, and humidities that are observed in a
given test. These calibration curves were obtained as follows:
Refri&:erant Pressure Calibration
A Bell and Howell dead weight pressure tester was used to accurately apply a full
range of pressures to each of the refrigerant pressure transducers. Transducer output
voltages were recorded for each pressure, and complete calibration curves were fonned.
Linear, least squares fits of the data provided a mathematical relationship between
transducer output voltages and refrigerant pressures. Figure 2.11 shows the calibration
curve fit for a 0-100 psi (0 to 690 kPa) refrigerant pressure transducer (S.N. 185502).
23
120
100
Oil 80 .r;;
.£:0 e ;:)
'" '" 60 £ "0 Q)
:a 40 <' 20
0 0
Aj)plied Pressure vs. Transducer Output Calibration - S.N. 185502 0-100 psig
................. Pre~sure [psig] = ~0.059 Volts -,0.054922 ..... + ........................ .
____T:l:;::.::~:l::,=~ __ J_ ----__ . ______ ... ______ .... 1. ___ ....... __ ..... __ ... ____ 1----------.... ____ ....... -..... _____ .......... __ ....... _____ ._ .... ____________ .
1 ·2 3 4 Transducer Output [Volts]
Figure 2.11: Refrigerant Pressure Transducer Calibration
Air Pressure Calibration
827.5
689.6
551.7 ~ "0 -..... 0 Q.
413.7 ~ '" '" c (2
275.8 ~ ..!::.
137.9
0 5
Since the air pressure transducers are designed to detect very small pressures (up to
5 in H20), a carefully measured water column was used to provide a pressure standard for
the calibrations. A full range of pressures was applied to each of the air pressure
transducers, and the corresponding output voltages were recorded. Linear, least squares
fits of the data provided a mathematical relationship between transducer output voltages and
air pressures. Figure 2.12 shows the calibration curve fit for a 0 to 5 in H20 (0 to 1245
Pa) air pressure transducer (S.N. 357836).
24
5
4
3
2
o o
Applied Pressure vs. Transducer O'!tput Calibration - S. N. 357836 0-5 in H20
Pressure '[in HP] = '1.0004 * Volts - 0.048827
Pressure [Pal = 249.10 * Volts - 12.157; : ····_-_········_-_···t···········_-_· __ ·····t······················-r············ __ ·-_······· .. -.. -.-........... -~-........... --.-.. -.-
1 1 j j
I I I I : :: :
-r--r--: --rr--
1 234 Transducer Output [Volts]
5
Figure 2.12: Air Pressure Transducer Calibration
Temperature CaL.Jration
6
1250
1000
~ 750 _. 8.. ~ CIl CIl
500 ~
~ 250
o
A Neslab RTE-220 temperature controlled water bath provided a wide range of
reliable temperatures for the thermocouple calibration. The corresponding thermocouple
voltage differences were observed and recorded, and a polynomial fit of the data was
developed. Figure 2.13 illustrates the results of the calibration procedure.
Dew Point Sensor Calibration
Dew point sensor calibration was performed by the manufacturer in accordance
with MIL-STD 45662A. Certificates of conformance indicate that the evaporator inlet and
outlet dew point sensors are accurate to +/- 0.36 OF (+/- 0.2 °C).
25
Temperature vs. Thermocouple Differential Voltage
40 104
35 ... Temp [F] = -1008840 V t2 + 45962.0 V + 32.3763····--f---------------ou i
95
30 ,-., u '" Q) 25 Q) .. !)/) Q) "0 '-" 20 ~ ;::l .... «l ..
15 Q) Q..
S
... Temp [C] ; -560467 V 00,' + 25534.4 V + 0.20906 ......... [ ....•...........
-----------------r-----------------·--------------------0-----------------""["----------------1-------------------------------------
86 ..., I'D
77 S
"0 I'D ..., ~ .... c
68 ..., I'D ,-., Q.. I'D
OQ
59 ..., I'D I'D
'" Q)
E-o 10 "Ij
50 '-"
5 ---------------- -------------------r----------------T----------------T-----------------r-----------------r--------------- 41
0 32 0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014
Differential Voltage
Figure 2.13: Thermocouple Calibration
Watt Transducer Calibration
The watt transducer calibration was perfonned by the manufacturer in accordance
with MIL-STD 45662A. A certificate of compliance guarantees accuracies of +/- 0.2% of
the power reading
2.3.10 Gas Chromatograph
The thennodynamic properties of a refrigerant blend are a function of the relative
amounts of each of the blend components. Therefore, a means of determining the mass
composition of the refrigerant in the system is required. A gas chromatograph cae) is
used for this purpose.
26
The heart of the GC system is a mainframe which uses a probe to measure the
thermal conductivity of the gases passing through a cell. The probe materials consist of
Tungsten and 3% Rhenium. A column consisting of 5% Krytox liquid phase on a
stationary support of 60/80 Carbo Pac B separates the components of the refrigerant blend.
This column is 1/8 inch (0.32 cm) in diameter and extends 24 feet (7.3 m) in length.
An integrator reads the mainframe output signal and plots the results. Figure 2.14
. shows an example integrator output. The area of the peak occurring at -3.5 minutes is
proportional to the mass percentage ofHFC-32 in the mixture. Correspondingly, the peaks
occurring at -6.3 and -6.6 are proportional to the mass percentages of HFC-125 and HFC-
134a respectively. In addition to the plot, the integrator also sends a results summary
directly to a desktop computer for storage.
System Samplin&
Before turning on the gas chromatograph, the carrier gas flow (99.999% pure
Helium) is established and a leak check is performed. The temperatures of the column,
detector and injection port are set to 50, 55 and 50 °Celcius respectively. The detector
current is adjusted to 150 milliamps. The GC is allowed to warm up for at least an hour
until the baseline zero reaches a steady value. Meanwhile, the flow rate of the carrier gas is
adjusted to 30 mLlmin using a bubble flow meter and stop watch.
The air conditioner testing facility is equipped with two service -qJves: one on the
liquid line to the expansion valve and the other on the compressor discharge line. A needle
valve and a length of plastic tub~ng are connected to each of these service valves. A gas
tight syringe equipped with a repeating adapter is used to penetrate the plastic tubing for
extracting nine microliter refrigerant samples. Before taking a sample, the refrigerant is
exhausted through the plastic tubing and into a beaker of water for at least 30 seconds.
While the refrigerant is flowing, the needle of the syringe is inserted into the tubing and the
plunger is moved its full length five to ten times. This ensures that the syringe is purged of
any gas contaminants. After extracting the sample, the syringe is removed from the tubing
and a septum is promptly placed on the tip to minimize sample contamination.
The syringe is transported immediately to the GC (-25 meters away). After
removing the septum, the syringe is inserted into the sampling port of the GC. The
integrator is started while the sample is injected into the port. The mass composition of the
sample is determined using the areas calculated by the integrator and the component mass
27
factors (see GC Calibration below). Representative results of the sampling are contained
in Table 2.3.
Table 2.3: Results of GC Sampling
ass ole ly 0 0 0 M ~ Cd all 23~ 115~ 152~)
Date R32 R125 R134a
June 7, 1994 22.5% 25.0% 52.5%
June 7, 1994 22.8% 24.8% 52.3%
February 21, 1995 22.6% 25.1% 52.3%
February 21, 1995 22.6% 25.1% 52.3%
March 8, 1995 22.4% . 25.1% 52.5%
GC Calibration
Quantities of each of the individual components of the mixture were obtained along
with the barometric pressure and temperature for the purpose of calibration. Measured
volumes were extracted from each of the containers and injected into an evacuated gas
collecting tube. Property routines contained within Engineering Equation Solver (EES)
Version 3.70 were used to calculate the density, and in turn, the mass of each component at
the measured pressure and temperature. A sample of this known mixture was then injected
into the Gc. Four different samples were injected. The maximum variation in area
percentage of any of the components was 0.37%. The output from the GC was then used
to calculate the mass fraction for each of the components. These fractions were 4.93xl0-
13, 7.95xlO-13 and 7.35xlO-13 lbm/area for R32, R125 and R134a respectively.
28
• RUri II . 52 FEB 21. 1995 13,56:87 START
If
3.'t97
PW
6.2S2
6.60'1
rIlIE1FlBlE STOP
Closing signal file M.SIGNAL .SNC Storing report to H:Q0140079.RPT
RUNU FE8 21, 1995 13,56,07
SIGNAL FILE, M:SIGNAl.BNC REPORT FILE: H,Q0110079.RPI FlFEA/'
ARER T'lP[ 29690 588 20669 PI}
4131 '1 U8
TOTAL AREA- 91673 NUL FRCTOR-l.0000[-00
IJI 0 r H .08'1 ,139 .1~7
Figure 2.14: Example Integrator Output
29
Chapter 3
Mathematical System Model Development
A mathematical system model was developed to predict the performance of an air
conditioner testing facility charged with a zeotropic refrigerant consisting of HFC-32,
HFC-125, and HFC-134a (23%, 25%, and 52% respectively). The following chapter
begins with a discussion of the system model inputs, outputs, and operating modes. It then
provides a detailed description of each of the component models used in the system
simulation. Next, the Newton Raphson program used to simultaneously solve the
component model equations is discussed. Finally, the overall system model results are
compared to actual data taken directly from the experimental facility.
3.1 Model Inputs, Outputs, and Operadng Modes
The system model inputs include operating parameters that are either controlled or
easily 'adjustable on the air conditioner testing facility; A summary of these inputs appears
in Table 3.1.
Table 3.1 System Model Inputs
Model Input Units
Evaporator Air Mass Flow Rate kgls
Evaporator Inlet Air Temperature CC
Evaporator Inlet Air Relative Humidity
Evaporator Inlet Air Pressure kPa
Valve Position turns
Compressor Speed RPM
Condenser Inlet Pressure kPa
Subcooling CC
30
Table 3.2 System Model Outputs
Model Output Units
Liquid Line Inlet Pressure kPa
Expansion Valve Inlet Pressure kPa
Evaporator Inlet Refrigerant Pressure kPa
Expansion Valve Enthalpy kJlkg
Evaporator Superheat 'C
Compressor Suction Pressure kPa
Compressor Suction Enthalpy kJlkg
Compressor Suction Temperature 'C
Refrigerant Mass Flow Rate kg/s
Sensible Capacity kW
Latent Capacity kW
Total Capacity kW
Evaporator Outlet Air Temperature 'C
Evaporator Outlet Air Relative Humidity
Compressor Power kW
Evaporator Air Pumping Power kW
System COP (inc. air pumping power)
A complete list of the system model outputs is shown in Table 3.2. Virtually all of
the performance related quantities that are measured on the air conditioner testing facility
have been represented as outputs of the simulation.
The input / output arrangement illustrated in Table 3.1 and 3.2 imitates the inputs
and outputs of the actual testing facility. Therefore, this model configuration is known as
facility mode. However, the simulation can be easily reconfigured to run in thermostatic
expansion valve mode. In this mode, the amount of superheat becomes an input to the
model while valve position becomes an output. The remaining inputs and outputs are left
unchanged. In this configuration, the system model can actually predict the performance of
the air conditioner testing facility with a thermostatic expansion valve installed. The details
of switching model inputs and outputs are discussed further in section 3.6.4.
31
3.2 Compressor Model Description
The compressor;model predicts compressor power and refrigerant mass flow rate
using a similar modeling approach to that of Darr and Crawford, 1992 [3]. The model
inputs include suction pressure, suction enthalpy, and discharge pressure. In addition, the
compressor speed, compressor displacement volume, and several empirical parameters are
used to provide accurate power and flow rate calculations. A diagram of the compressor
model is shown in Figure 3.1 followed by a detailed description of the compressor flow
rate and power prediction techniques.
Physical Parameters . compressor spee d
c ompressor displacement -
Inputs ,r , r
e ... suction pressur
suction enthalpy
discharge pressur
- Compressor - Model -.... ..
Figure 3.1: Compressor Model Diagram
3.2.1 Predicting Refrigerant Mass Flow Rate
... .. .-
~
Outputs
compressor power
refrioerant mass flow rate
The compressor suction volumetric flow rate can be represented as:
32
. v = l1volNV disp
where:
• V == Volumetric Flow Rate
11 vol == . Volumetric Efficiency
N == Compressor Speed V disp == Compressor Displacement Volume
(3.1)
Since displacement and compressor speed are known, the refrigerant flow rate can be
obtained with an empirically based prediction of compressor volumetric efficiency.
Developin2 an Expression for Predictin2 Volumetric Efficiency
A functional relationship between volumetric efficiency and other model variables
was developed using an approach similar to that of Martin [4]. He demonstrated that the
volumetric efficiency of a constant speed reciprocating compressor is a simple linear
function of the ratio of the discharge pressure to the suction pressure. The compressor in
this study is operated at varying speeds from 2300 to 3450 RPM, so an additional linear
term including compressor speed was necessary in the correlation. The volumetric
efficiency model takes the form:
where:
11 vol == Volumetric Efficiency
P d == Discharge Pressure
P == Suction Pressure s
N == Compressor Speed
N ref == Reference Compressor Speed (3450 RPM)
33
(3.2)
Using data taken directly from the testing facility with discharge-to-suction pressure
ratios ranging from 1.99 to 2.84 and compressor speed ratios ranging from 0.67 to 1.00,
the following empirical parameters were obtained.
C1 = -0.104112
C2 = -0.062225
C3 = 1.094268
A graphical representation of the volumetric efficiency expression (equation 3.2)
appears in Figure 3.2. Figure 3.3 shows the agreement between experimentally determined
volumetric efficiency and the corresponding predicted values. Results indicate that
volumetric efficiency prediction accuracies of +/- 2% can be expected.
0.83
0.82
0.81 :>. 0 c (J) 0.8 0
:;:: -w 0 0.79 ''::: -(J) E ::::I 0.78 '0 >
0.77
0.76
0.75 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9
Pressure Ratio
Figure 3.2: Volumetric Efficiency vs. Compressor Speed & Pressure Ratio
34
>. u c (I)
·u :E UJ u ·c +-' (I)
E ::l
(5 > -C (I) +-' U :0 (I) .... c..
0.86
0.84
0.82
0.8
0.78
0.76
0.74
0.72 0.72 0.74 0.76 0.78
1. 99 ::;; P discharge::;; 2. 84 PSUCtiOD
N O. 66 ::;; compressor::;; 1. 00 N ref .
0.8 0.82 0.84
Experimental Volumetric Efficiency
Figure 3.3: Volumetric Efficiency Prediction Accuracy
A Comment on Volumetric Efficiency Models
0.86
The refrigerant flow rate prediction method implemented by Darr and Crawford [3]
involves calculation of an isentropic volumetric efficiency. It was not used in this system
model, however, since it requires knowledge of an unobtainable parameter - the
compressor clearance volume. The isentropic volumetric efficiency approach is very likely
preferred over the previously described method when compressor dimensions are available.
35
3.2.2 Compressor Power Prediction
The compressor power is predicted by combining the previously determined
refrigerant flow rate with refrigerant suction density and a prediction of the actual work of
compression.
P comp = V . Psuction • W comp (3.3)
where:
P comp == Compressor Power
V == Suction Volumetric Flow Rate
P suction == Suction Refrigerant Density
w comp == Actual Work of Compression
Predictin& the Actual Work of· Compression
The actual work of compression is predicted using the isentropic work efficiency
approach described by Darr and Crawford [3]. Isentropic work efficiency is defined as
follows:
where:
w c-s == Isentropic Work of Compression
w c == Actual Work of Compression
(3.4)
The isentropic work of compression is defined as the work per unit mass of
refrigerant required to isentropically compress the incoming refrigerant from the suction
pressure to the discharge pressure. It can be easily calculated using the known compressor
suction conditions and discharge pressure.
36
where:
w c-s == Isentropic Work of Compression
hs == Compressor Suction Enthalpy
hd- s == Enthalpy at Discharge Pressure and Suction Entropy
(3.5)
The actual compressor shaft work per unit mass of refrigerant, w c' is calculated
using the following expression.
W w =_c c . (3.6)
m
where:
VI c == Compressor Shaft Power
m == Refrigerant Mass Flow Rate
Since a hermetic compressor is used on the testing facility, the actual compressor
shaft power cannot be determined directly using torque and shaft speed measurements. Instead, it is estimated using the available inverter input power measufement, Pinverterin'
along with the compressor motor and inverter efficiencies.
VI c = llinverter . llmotor . P inverter in (3.7)
The motor efficiency, llmotor' is assumed constant at 0.9. The inverter efficiency, llinverter'
is estimated from manufacturer's data. Figure 3.4 shows the estimated inverter efficiency
as a function of motor speed.
37
0.99
0.98
» 0.97 o c CD o -iii 0.96 ~
CD -~ CD > c 0.95
0.94
0.93
1500
--11-'
I[-r ---rrr
2000 2500 3000
Compressor Speed
Figure 3.4: Inverter Efficiency vs. Compressor Speed
3500
A suitable expression for predicting isentropic work efficiency is a simple linear function of
both discharge-to-suction pressure ratio and compressor speed ratio.
where:
llw-s == Isentropic Work Efficiency
P d == Discharge Pressure
P == Suction Pressure 5
N == Compressor Speed
N ref == Reference Compressor Speed (3450 RPM)
38
(3.8)
Using actual compressor data with discharge-to-suction pressure ratios ranging
from 1.99 to 2.84 and compressor speed ratios ranging from 0.67 to 1.0, the following
parameters were obtained.
C4 = 0.09940
Cs = -0.24169
C6 = 0.60555
A graphical representation of the isentropic work efficiency expression (equation
3.8) is provided in Figure 3.5. A comparison of predicted and experimentally determined
isentropic work efficiencies is illustrated in Figure 3.6. Results indicate that isentropic
work efficiency predictions within +/-2% can be expected.
>. o c Q) ·0 ;;::::
w
o Q. o ~ -c Q) (J)
Figure 3.5:
0.72
0.7
0.68
0.66
0.64
0.62
0.6
0.58 2.1 2.2 2.3 2.4 2.5 2.6 2.7
Pressure Ratio
Isentropic Work Efficiency vs. Compressor Speed and Pressure Ratio
39
2.8 2.9
0.72
0.7
>. u c:: Q)
'u 0.68 i.i=
\I-UJ ~ ... 0 3: u 0.66 '0. 0 ... +-' c:: Q)
J!!. 0.64 "0 P discharge Q) 1.99 :::;; :::;;2.84 +-'
U Psuction '5
Q)
N com£ressor ... a.. 0.62 0.66:::;; :::;;1.00
N ref.
0.6 0.6 0.62 0.64 0.66 0.68 0.7 0.72
Experimental Isentropic Work Efficiency
Figure 3.6: Isentropic Work Efficiency Prediction Accuracy
40
3.3 Heat Exchanger Models
3.3.1 Evaporator Model
An air-to-refrigerant heat exchanger model developed by Ragazzi [5] is used in the
system simulation. The model solves the coupled heat transfer, mass transfer, and
refrigerant pressure drop equations for each individual heat exchanger tube pass using a
Newton Raphson routine. The model begins by assuming that the inlet air conditions to
each tube pass is the same as the overall heat exchanger air inlet condition. A successive
substitution procedure is then used to solve for the actual inlet air conditions to each tube
pass.
The heat exchanger model has been validated experimentally. Results show
excellent agreement between predicted and actual heat exchanger performance for two coils
with significantly different geometries. Because of the tube-by-tube approach used in the
model, changes in coil circuitry can be simulated with a high level of confidence.
3.3.2 Condenser I Sub cooler Model
Unlike a typical air conditioning systn, the operator of the experimental test
facility can fix the system condenser pressure by setting the condenser pressure controller
and adjust the amount of refrigerant subcooling using the subcooler water control valve.
Likewise, condenser inlet pressure and degrees of subcooling are parameters in the system
model. Therefore, equations modeling the heat transfer in the condenser and subcooler are
unnecessary for predicting system performance. The enthalpy of the refrigerant leaving the
subcooler and entering the expansion device can be determined using the model parameters
and an accurate expression for pressure drop in the condenser and subcooler.
3.4 Pressure Drop Calculations
Section 3.3.2 points out that a complete condenser model is not needed to
accurately model the performance of the experimental facility. However, although it is not
41
necessary to model the heat transfer in the condenser and subcooler, an expression for the
pressure drop in the heat exchangers is required. In addition, a inodel of the expansion
device is needed to complete the system simulation. The details of these pressure drop
models appear in the following sections.
3.4.1 Condenser I Subcooler I Liquid ·Line Pressure Drop
A condenser I subcooler pressure drop expression was developed using the
condensing two phase correlation described by Paliwoda, 1989 [6]. The method consists
of two simple steps. First, the Darcy-Weissbach formula is used to calculate the pressure
drop for saturated refrigerant vapor alone flowing through the condenser.
ALG2'\) AI> =---
vapor 2d H
where:
A. == Single Phase Friction Coefficient
L == Condenser Tubing Length.
G == Refrigerant Mass Flux
'\) == Refrigerant Vapor Specific Volume
dH == Condenser Hydraulic Diameter
(3.9)
Since a single phase friction factor correlation for the enhanced, coaxial condenser and
subcooler coils was not available, a correlation was created using experimental data.
A. = 470 Re-Q.480 (3.10)
Secondly, this single phase pressure drop is multiplied by a condenser 2 phase
correction coefficient, ~m.
~m =0.36(9+1) (3.11)
where:
42
_ '\)' ('TI' )0.25 8-- -
'\) 'TI
'\) == Refrigerant Specific Volume
'TI == Refrigerant Viscosity
, " Saturated Liquid and Vapor Respectively
(3.12)
Upon leaving the subcooler as subcooled liquid, the refrigerant must pass through a
liquid line solenoid valve, several 90 degree elbows, and approximately 4 meters of 0.43
inch (1.1 cm) I.D. copper tubing. The pressure drop in these components is small relative
to the condenser / subcooler pressure drop. Therefore, a simple pressure drop calculation
with an experimentally determined, constant friction factor provides sufficient accuracy.
CG2'\)
AI> Uquid Une = -2-
where:
C = 65.166
G == Refrigerant Mass Flux
'\) == Refrigerant Liquid Specific Volume
(3.13)
Figure 3.7 illustrates that the overall pressure drop prediction in the condenser,
subcooler, and liquid line is accurate to within +/- 10%.
3.4.2 Expansion Device I Distributor Pressure Drop
The refrigerant expansion occurs in three components: a precision needle valve, a
distributor manifold, and distributor tubing. Paliwoda [7] presents a method for predicting
two-phase pressure drops across pipe components similar to the method that was used to
predict condenser pressure drop. First, a single phase pressure drop across the component
is calculated. This single phase pressure drop is then corrected using a two-phase
multiplier. The method assumes that quality is fairly constant across the pipe component of
interest. This assumption is reasonable for the relatively small pressure drop in the
distributor tubing. However, Paliwoda's method is not applicable for the pressure drop in
43
140
'ii 120
a. ~ ...... Q. 0 ... Cl 100 G) ... ::s I/) I/) G) ... a. '0 80 G) .. 0
=0 G) ... a.
60
40 40 60 80 100 120 140
Actual Pressure Drop [kPa]
Figure 3.7: Condenser I Subcooler I Liquid Line Pressure Drop Agreement
the needle valve and the distributor manifold since refrigerant quality changes significantly
across these components.
Before exploring other, more complicated, two-phase pressure drop calculation
techniques for the needle valve and distributor manifold, a simple pressure drop expression
assuming single phase liquid refrigerant flow was considered. The method proved to be
surprisingly reliable. Upon further investigation, however, the accuracy of the single
phase correlation was justiUed. According to Stoecker and Jones [8], although the
refrigerant following the throttling process in the expansion valve is two phase, the
vaporization does not occur until after the fluid has passed through the valve. Within the
valve, the refrigerant remains in a metastable liquid condition. The pressure drop in the
needle valve and distributor manifold is calculated using expression 3.14. The flow
friction coefficient, C, is a function of valve position as shown in equation 3.15. The
relationship was developed with experimental data for valve positions ranging from 3 to 8
turns.
44
where:
C = 429 e-O.684(Valve Position) + 18.32
G == Refrigerant Mass Flux
based on 0.125 in (0.318 cm) valve orifice diameter
u == Refrigerant Liquid Specific Volume
(3.14)
(3.15)
Note: Valve Position represents expansion valve position in number of turns.
The pressure drop in the distributor tubing is calculated using a variation of the two
phase multiplier method used in the condenser pressure drop expression.
where:
A. = 0.3164 Re -{).25 (Blasius formula)
L == Tubmg Length
G == Refrigerant Mass Flux
u == Refrigerant Vapor Specific Volume·
d == Tubing Inside Diameter
1
B = [8 + 2(1- 8)x](I- X)3 + x3
x == Refrigerant Quality
=~(~)O.25 8 .. .. u 11
u == Refrigerant Specific Volume
11 == Refrigerant Viscosity
I " Saturated Liquid and Vapor Respectively
45
(3.16)
(3.17)
(3.18)
(3.19)
(3.20)
The overall pressure drop in the needle valve, distributor manifold, and manifold
tubing can be predicted within +/- 7% as shown in Figure 3.8.
1400
'iii' Il. ~ 1300 c. 0 ... 0 Q) 1200 ... ::J (/) (/) Q) ... Il. 1100 Q) 0 ';; Q)
0 1000 c: 0 'iii c: as 900 c. x W
'C Q) - 800 0 =c Q) ... Il.
700 700 800 900 1000 1100 1200 1300 1400
Experimental Expansion Device Pressure Drop [kPa]
Figure 3.8: Expansion Device Pressure Drop Agreement
3.5 Air and Refrigerant Properties
All of the component models in the system simulation require air and/or refrigerant
properties. Air properties and refrigerant thermophysical properties are calculated using
subroutines developed by Ragazzi [5]. Refrigerant thermodynamic properties are linearly
46
interpolated from tables generated with a computer program known as REFPROP (Version
4.0) [9, 10].
3.6 ACRC Newton Raphson Solver
The mathematical system model uses an ACRC developed Newton Raphson solver
written in Fortran to solve the simultaneous component model equations. A thorough
explanation of the Newton Raphson method of solving algebraic, nonlinear equations is
given by Stoecker, 1989 [11]. The solver is equipped with several helpful features such as
automatic step relaxation, mid-solution equation switching, pre/post processing of the
solver inputs and outputs, and the ability to produce spreadsheet readable outputs.
The ACRC solver input/output is handled through the use of either variables or
parameters. Variables appear in the residual equations, and their values are determined
numerically using the Newton Raphson technique. In contrast, parameters are either user
specified values that act as inputs to the set of simultaneous equations or outputs of the
solver whose values could be directly and sequentially calculated. It is important to
understand the distinction between variables and parameters when using the ACRC solver.
Operation of the ACRC solver requires knowledge and manipulation of seven files:
EQNS.f, CHECKMOD.f, XK, EQUIVLNT.INC, INITMOD.f, SLVRSET, and INSTR.
A brief description of the purpose and format of each file follows. Detailed information
regarding the solver and its advanced features is given by Mullen, 199· r12].
3.6.1 EQNS.f
EQNS.f holds the CALCR subroutine which contains the simultaneous equations
that should be solved using the Newton Raphson method. The equations must be written
in residual format. For example, suppose the first equation takes the form
Left Hand Side = Right Hand Side
The corresponding equation in residual format is
R( 1) = Right Hand Side - Left Hand Side
47
The equation is solved when the residual value approaches zero. Appendix F contains the
CALCR subroutine for the mathematical air conditioning system niodel.
3.6.2 CHECK;MOD.f
Checkmod.f contains three subroutines: IC, BC, and FC. IC is called prior to the
Newton Raphson solver routine, and contains all necessary preprocessing operations. BC
is called before each Newton Raphson step is taken. The BC subroutine can be used to
impose boundaries on Newton Raphson variables or parameters. BC may also perform
mid-solution equation switching based on the NR variable values by presetting logical flags
that "switch" model equations in the CALCR subroutine. FC contains all post processing
of variable or parameter values. The mathematical air conditioning system model uses the
FC subroutine for post processing (see Appendix F).
3.6.3 EQUIVLNT.INC
The solver uses an array (XK) for primary storage of each of the parameter and
variable values. To improve equation readability, Equivalence statements located in the
EQUIVLNT.INC file assign meaningful names to each of the elements in the XK array for
use in the solver subroutines (CALCR, IC, BC, and FC). Appendix F contains the
EQUIVLNT.INC file for the mathematical air conditioning system model.
3.6.4 XK
The variable and parameter initialization file (XK) defines whether a quantity is a
variable or a parameter in the solution. Variables are flagged with an "X" in the second
column of the XK file while parameters are flagged with a "K". The file also contains the
initial value of each of the variables and parameters. In addition, it holds details regarding
the output format of each variable and parameter including the number of significant digits
displayed, the units on the quantity, and the option to remove the variable or parameter
from the output. Appendix F contains the variable and parameter initialization file for the
air conditioner system model.
48
Variable and Parameter Swannina:
The Newton Raphson method requires a number of non-singular, independent
equations along with the same number of unknown variables. As long as the equations
remain non-singular and independent, a model input parameter can be changed to an
unknown variable if, simultaneously, a former variable is changed to a model parameter.
The ACRC Newton Raphson solver has been written to take advantage of this
flexibility. Model variables and parameters can be swapped by simply exchanging the
corresponding "K" and "X" flags in the variable and parameter initialization fIle (XK). For
further explanation of variable and parameter swapping, see Mullen, 1994 [12].
3.6.5 INITMOD.f
INITMOD.f holds the InitializeModel subroutine which reads the XK initialization
file and prepares the program to solve the system of equations in the CALCR subroutine.
It is here that the total number of variables (NumVar) and total number of parameters
(NumPar) are declared. These totals must reflect the number of variable and parameter
declarations in the XK fIle. In addition, the InitializeModel subroutine can be used to call
other initialization subroutines required for the solution of the residual equations. For
example, InitializeModel may call a subroutine which initializes thermodynamic property
routines for a set of residual equations that represent a thermal system. Appendix F
contains the InitializeModel subroutine for the air conditioner system model. For
convenience, the statements that were changed or added to accommodate the air conditioner
system model are highlighted.
3.6.6 SL VERSET
SL VERSET allows the user to set solver parameters, residual equation convergence
criteria, and output options. A sample SL VERSET fIle appears in Appendix F.
49
3.6.7 INSTR
The instructions file (INSTR) directs the execution of the ACRC solver. Four
types of analysis can be performed on the system of equations: single analysis, multiple
analysis, sensitivity analysis, and uncertainty analysis. Single and multiple analysis will be
briefly described in the following paragraphs. Detailed information regarding all four
analyses is given by Mullen, 1994 [12].
SinKle Analysis
Single analysis solves the set of residuals equations using one set of input
parameters. The typical single analysis instruction file contains only three lines. An
example follows:
SINGLE XK out
The word "SINGLE" instructs the program to solve the equations for a single set of input
parameters. "XK" is the name of the variable and parameter initialization file. This file
should reflect the parameter values and variable initial guesses preset by the user for
solving the residual e"'uations (see XK description above). The final line in the single
instructions file. contains the output file extender. In this case, the extension ".out" will be
added to all solver output filenames.
Multiple Analysis
Multiple analysis allows the user to run several combinations of equation input
parameters at a time. A typicai multiple analysis. instruction file follows:
MULTIPLE XK mIt 3,2,0 1, 5 5.5, 3450.0 5.0, 3175.0 4.5, 3000.0
50
The word "MULTIPLE" instructs the program to solve the equations for several sets of
input parameters. "XK" and "mlt" are the initialization file and output extender as
described for single analysis. Line four tells the solver the number of solutions to perform,
the number of parameters that will be varied, and the number of intermediate steps to take
between solutions. The fifth line contains the XK array indexes that correspond to the
·parameters that will be varied. Each of the remaining lines contain a complete set of
parameter values for the multiple run analysis.
3.7 System Model Validation
In order to gain confidence in the interaction between each of the previously
described component models, the overall system model results were compared to data
collected experimentally. Table 3.1 shows the range of conditions that were explored in the
validation. Although the system was validated for only one set of air inlet conditions, the
wide range of evaporator pressures (639 - 793 kPa) and refrigerant flow rates (0.051 -
0.072 kg/s) that were observed verifies the evaporator model's ability to accurately predict
refrigerant outlet conditions. For additional confidence in the performance of the
evaporator simulation, refer to Ragazzi [5].
Table 3.1: System Model Validation Input Ranges
Condensing .Pressure 1475 - 2050 kPa (214 - 297 psia)
Com~ressor Speed 2300 - 3450 RPM
Expansion Valve Opening 3.5 - 6.0 turns
Subcooling 3.5 - 9.7 °C (6.3 - 17.5 OF)
Air Mass Flow Rate 0.73 kg/s (5800Ibslhr)
Air Inlet Temperature 32°C (90 oF)
51
Figure 3.9 compares the experimental and predicted refrigerant mass flow rates. As
the plot shows, 93% of the predicted flow rates fell within +/- 4% of the corresponding
experimental value.
Vi ....... Cl ~ (J) -as a: :: 0 u: -c as ... (J) Cl ·c -(J) a: a; 'C 0 ~
0.075
0.07
0.065
0.06
0.055
0.05 0.05 0.055 0.06 0.065 0.07
Experimental Refrigerant Flow Rate [kg/s1
Figure 3.9: Refrigerant Mass Flow Rate Comparison
52
0.075
Figure 3.10 compares the predicted and experimental evaporator capacities. All of
the predicted capacities fell within +/- 4% of the experimentally measured evaporator load.
13
12.5
§' 12 ::t:.
~
>. -0 ra 11.5 0. ra 0 ~
0 11 -ra ~
0 0. ra
10.5 > w Q)
"C 0 10 ~
9.5
9 9 9.5 10 10.5 11 11.5 12 12.5 13
Experimental Evaporator Capacity [kW]
Figure 3.10: Evaporator Capacity Comparison
53
The predicted and measured evaporator pressures are compared in figure 3.11. In
all cases, predicted evaporator pressure fell within +/- 4% of the corresponding measured
value.
as a.. =. Q) ... :::J II) II) Q) ... a.. ... 0 .... as ... 0 a. as > w Q) "C 0 ~
850
800
750
700
650
600 600 650 700 750
Experimental Evaporator Pressure [kPa]
Figure 3.11: Evaporator Pressure Comparison
54
800 850
Figure 3.12 shows the agreement between predicted and measured compressor
power. As shown, compressor power was predicted within +/- 4% for all cases.
3.4
3.2
~ 3 ~ .... CD ~ 2.8 0 a.. .... 0 If)
2.6 If) CD .... 0. E 0 2.4 ()
CD "C 0 2.2 :2
. . . . . .
~~_=-I::]~::I=r:~~~-~~--=~ ! : : :' :
iii i i 1 ! ! 1 j --_· __ ············t···················t··········· .. ····_-t····················[······· .... 0 •• to •••••••••••••••••• [ •••••••••••••••••••• [ ................. .
I I , i . I I
~:l=+=l=~-=+~:=-=r=:: .................. 1......... .. ..... : ... -e:. . ........ + ................... .l. ................. .J .................. .J ................... .l. ................ . . . . . , . .
: : : : : : :
2 : 0: I Iii i -••••• -.-••• , ___ 0'- •••••••••• -:----••••••••••••••• -4-- ••••••••• --••••••• ,. •••••••• -••• - ....... ~ ••••••• -.-............ ; •• -......... - ••• •••• jo ................. .
, , , , I I 1.8
1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4
Experimental Compressor Power [kW]
Figure 3.12: Compressor Power Comparison
55
Figure 3.13 compares actual and predicted values of COP. Predicted COP fell
within +/- 4% of the measured value in all cases.
a.. o ()
Gi "8 :E
6
5.5
5
4.5
4
3.5
3 3
·························r·························r·························r·························"["···· ....................................... .
I I I ; .
~=[-=L-~~~~-~~~J-~--~~ 1 i i! :: :: :: ::
1: l! .-.--•••••• ----------.---~-------••••••• -.- - ••• 0. ._--- ._._._._---------+ ... ---------.. -------------l--_.n---------_._---------l-------------------------
I 0 I I I · . . · . . · . . ._._ ... __________ .. _______ . __ .. _____ ...... __ .:. ... ____ . ____ ... ______ ..... 1. __ ........ __________ .... __ L ___ . _____ ..... _________ . ___ L. ______________ . ________ .
3.5
I I I I : : : :
4 4.5
Experimental COP
5 5.5 6
Figure 3.13: COP Comparison
56
Chapter 4
System Performance and Control Analysis
The main objective of this work is to investigate the performance and control of
split system air conditioners charged with a refrigerant mixture of HFC-32, HFC-125, and
HFC-134a (23%, 25%, and 52% respectively). The first part of this chapter addresses the
performance issue by analyzing the potential performance gains that can be realized with
improved air-to-refrigerant temperature glide matching in the evaporator through changes in
heat exchanger design. The second section quantifies the performance changes that result
from controlling the operating parameters of an air conditioner charged with the zeotropic
mixture.
4.1 Effect of Evaporator Design on System Performance
Zeotropic mixtures are considered to be a promising replacemE..,t for HCFC-22 due
to their characteristic temperature glide during an isobaric phase change. A better match
between the temperature profiles, of the refrigerant and the external fluid could result in a
reduction of heat exchanger irreversibilities and lead to an increase in system efficiency.
The level of irreversibility of various evaporator designs was quantified by Ragazzi [5].
Six evaporator coils with varying tube arrangements were evaluated with both pure and
mixed zeotropic refrigerants. In particular, the number of evaporator rows was increased
to approach a counterflow heat exchanger design which should result in improved air-to
refrigerant temperature glide matching. Figure 4.1 describes the coil geometries considered
in the study. Total heat transfer area and tube length were held constant in all cases while
the depth of the coil and the corresponding change in face area were varied.
57
air ~
32.99mm ,-. (1.299 in.)
air ~
refg.
refrigerant
o Flow out of the page
• Flow into the page
Figure 4.1: Circuitries of Cross-Counterflow Evaporator Coils with 2, 3, 4, 6, 9, and 12 Rows
According to Ragazzi [5], evaporator thermodynamic performance depends on the
number of rows for both HCFC-22 and the zeotropic mixture considered in the study.
However, the nature of this dependency does not vary significantly between the two
refrigerants. He concludes that the reduction in irreversibilities associated with improved
glide matching due to an increased number of evaporator rows are overshadowed by other
effects such as variations in air-side heat transfer coefficients.
The heat exchanger designs used by Ragazzi in his second law analysis (Figure
4.1) are considered in the current study. In this case, rather than quantifying heat
exchanger performance from a second law standpoint, each heat exchanger is included in
the system simulation to evaluate overall system performance from a fIrst law effIciency
standpoint. Table 4.1 shows the evaporator loading conditions and system operating
parameters that are enforced. For the purposes of this study, compressor volumetric
effIciency and isentropic work effIciency are held constant at 0.75 and 0.65 respectively.
Since this study focuses on variations in system performance resulting from changing
58
evaporator design, compressor efficiencies are held at these typical values to prevent
compressor-specific effects from influencing the simulation results.
Table 4.1: Loading Conditions and Operating Parameters
Loading and Operating Parameter Value
Evaporator Air Mass Flow Rate 0.567 kg/s (4500Ibmlhr)
Evaporator Inlet Air Temperature 32.2 °C (90.0 OF)
Evaporator Inlet Air Relative Humidity dry
Evaporator Inlet Air Pressure 101.35 kPa (14.696 psia)
Evaporator Superheat 5.5 °C (10 OF)
System Capacity 10.5 kW (36,000 Btulhr)
Condenser Inlet Pressure 1900 kPa (275 psia)
Figure 4.2 shows the compressor and air pumping powers that result from varying
evaporator tube arrangement in a system charged with a zeotropic mixture of HFC-32,
HFC-125, and HFC-134a (23%,25%,52%). The graph illustrates that the minimum total
system power required to produce an evaporator capacity of 10.5 kW is provided with the
nine row evaporator coil. This minimum presents itself due to the competing effects of
decreased compressor power caused by improved evaporator performance and increased air
pumping power due to higher evaporator coil air velocities. Figure 4.3 illustrates the
effects of varying the number of coil rows on system coefficient of performance (COP) as
defined in expression 4.1. System COP variations of approximately 15% are observed as
the number of heat exchanger rows change.
COP = ____ T_o_t_al_S....::.y_st_e_m_C---=ap'-a_c_ity~ __ _ Compressor Power + Air Pumping Power
(4.1)
At first glance, it may appear that improved air-to-refrigerant temperature glide
matching causes improved system efficiency as the number of evaporator rows increases.
However, Figure 4.4 indicates that other effects are playing a role in the system efficiency
trends. The graph shows system COP values obtained for the previously described
evaporator coils and operating conditions with HCFC-22 as the refrigerant. HCFC-22 is a
59
pure refrigerant without a characteristic temperature glide. Therefore, air-to-refrigerant
temperature glide matching should not improve as the number of evaporator rows
increases. Since the zeotrope and HCFC-22 results show nearly identical efficiency trends,
Ragazzi's conclusion is supported. As the number of evaporator rows increases, the
improvement in exchanger performance associated with improved glide matching are
overshadowed by other effects such as increased air-side heat transfer coefficients.
Note: The COP values shown in Figures 4.3 and 4.4 should not be
compared directly since they result from two different condenser operating
temperatures.
3.5
3
2.5
"-(I) 2 3: o a..
1.5
0.5
o 2 3 4 6 9 12
Number of Rows
Figure 4.2: Effects of Varying Tube Arrangement on Compressor Power and Air Pumping Power using Zeotropic Mixture of HFC-32, HFC-125, HFC-134a (23%, 25%, 52%)
60
5
4
3
2
o 2 3 4 6 9 12
Number of Rows
Figure 4.3: Effects of Varying Tube Arrangement on System COP using Zeotropic Mixture of HFC·32, HFC·125, HFC·134a
4
3.5
3
2.5
2
1.5
0.5
o 2 3 4 6
Number of Rows
Figure 4.4: Effects of Varying Tube Arrangement on System COP using HCFC·22
61
4.2 System Control Analysis
The split system air conditioner model is useful for evaluating system control
strategies. By varying the refrigeration system operating parameters and analyzing the
results, conclusions can be drawn regarding the control of air conditioner performance.
The following two studies focus on the control of three system operating
parameters: expansion valve position, compressor speed, and evaporator air flow rate.
The first study is conducted infacility mode where expansion valve position is a direct
model input. It quantifies the system performance variations that result from controlling
expansion valve position and evaporator air flow rate. The second study is conducted in
thermostatic expansion valve mode where refrigerant throttling is automatically adjusted to
provide a desired evaporator superheat. In this case, system performance changes resulting
from variations in compressor speed and evaporator air flow rate are considered.
4.2.1 Valve Position and Evaporator Air Flow Rate Control
This section discusses the air conditioner performance changes that result from
varying expansion valve position and evaporator air flow rate. Table 4.2 summarizes the
system loading conditions and operating parameters that are evaluated in the study, and
Figures 4.5 through 4.9 illustrate the simulation results. These results provide an
understanding of the ways that refrigerant throttling and evaporator air flow rate affect total
air conditioner capacity, sensible heat ratio, and overall system efficielwY.
Table 4.2: System Loading Conditions and Operating Parameters
Loading and Operating Parameter Value(s)
Evaporator Air Mass Flow Rate 0.35 - 0.73 kg/s (2778 - 57941bmlhr) (0.02 kg/s increment)
Evaporator Inlet Air Temperature 28.3 °C (83.0 oF)
Evaporator Inlet Air Relative Humidity 62%
Evaporator Inlet Air Pressure 101.35 kPa (14.696 psia)
Expansion Valve Positions 4, 5, 6, 7
Compressor Speed 3450 RPM
Condenser Inlet Pressure 1750 kPa (254 psia)
Subcooling 4.0°C (7.2 oF)
62
Discussion of Simulation Results
Figure 4.5 shows the total and latent evaporator capacity for several expansion
valve positions and evaporator air flow rates. It shows that the total capacity of the air
conditioner system is a relatively strong function of expansion valve position. A decrease
in expansion valve opening results in a lower refrigerant mass flow rate and, therefore, a
lower total evaporator capacity. Figure 4.5 also shows that total system capacity is a weak
function of evaporator air flow rate - especially for larger expansion valve openings. When
the system capacity and evaporator superheat graphs (Figures 4.5 and 4.6) are considered
simultaneously, it becomes evident that evaporator superheat increases caused by rising
evaporator air flow rates result in slight increases in total system capacity.
The sensible heat ratio of the air conditioner is a function of evaporator air flow rate
as shown in Figure 4.7. As evaporator air flow rate increases from 0.35 to 0.73 kg/s, the
ratio of sensible capacity to total capacity increases from approximately 0.48 to 0.58.
System COP reductions result from decreases in expansion valve position. Figure
4.8 shows the effects of varying expansion valve position and evaporator air flow rate on
compressor and air pumping power. It illustrates that compressor power declines with
reduced expansion valve opening. This trend is due to the resulting decreases in refrigerant
mass flow rate. However, while mass flow rate reductions cause compressor power to
decline, they also cause large system capacity decreases. Therefore, decreases in
expansion valve opening result in significant COP reductions as shown in Figure 4.9.
System COP is also affe~ted by evaporator air flow rate as shown in Figure 4.9.
Slight COP gains occur in areas where increased evaporator air flow rates cause slight
capacity gains. In these areas, increases in total system capacity and smaller increases in
compressor and air pumping power cause system COP to increase. However, as
evaporator air flow rate continues to increase, COP drops as the air pumping power
becomes increasingly significant.
63
14
0 1.',.0 0 0 0 oio 0 oio 0 0 0 i i 0 DiD 0 0 0 DiDO 0 0 DiD 0
12 .......................... B.j.D .... g .... ~ .............. ·f·········· .......... ············f······ .. ·· .... ··················j··· ...... · .................... . o 0 010 0 0 0 010 0 0 0 01 0 0 0 0 010 0
1 0 ............ X ... X··.x.I·X .. X .. X ... X·,X·f·>.CX ... x. .. X ... xtx. .. x.··X ... X .. xj.x..,X .................. .
0 Latent (Valve @ 7 turns) 0 Latent (Valve @ 5 turns) 0 Total (Valve @ 7 turns) ¢ Total (Valve @ 5 turns) 0 Latent (Valve @ 6 turns) x Latent (Valve @ 4 turns) 0 Total (Valve @ 6 turns) x Total (Valve @ 4 turns)
6 DiD 010 0 1 1 ............................... , ........ O .... D····B-.. ·!l·.;.·o ........ · .. O'···B-.. ·o.+ ............................... + ............................. . o 0 oio 0 i 0 0 0 i O 0 0 0 i
, 0 0 0'0 0,0 0 0 0 0,0 0 x xii 0 0 0 0 10 0 0 DiD 0
x1x x x x 1 1 0 01
I xix x x x xix x x x xl: ~ 4
0.3 0.4 0.5 0.6 0.7 0.8
Air Mass Flow Rate (kg/s)
Figure 4.5: Total and Latent Capacity Resulting from Varying Expansion Valve Position and Evaporator Air Flow Rate
64
5' f/) CD CD ... Cl CD :!:!. -as CD .r:. ... CD Q. ::J en ... o -~ o Q. as > w
25
20
15
10
5
x x xix x x x xix x x x xix x mmmfmmmjmm_t-mmmmmimmmmmm-I ! .
o 0 •••••••••• _ •••••••••• _ ••• __ •••••••••••••••••••••••••••••• __ ....................... ______ ••• __ • _______ ........................ _ ••••••••••••• __ •••••• 0.
o 0 o 0 o 0 o 0
Expansion Valve Position
--mTm--~mmmmr-~i ~~~
0.4 0.5 0.6 0.7 0.8
Air Mass Flow Rate (kg/s)
Figure 4.6: Evaporator Superheat Resulting from Varying Expansion Valve Position and Evaporator Air Flow Rate
65
0.7
0.65
0.6
0 ;: as 0.55 a: -as Q)
I 0.5 Q)
:c 'iii c: 0.45 Q)
rIJ
. , . .
=:=I:=r~~r==~~:::: i 1 i ----r: . ·-r-
-----·,-----i-=I~~l~~n-: 0.4 ............................... , ...................... ··········"1················,··············l············ -!-~ :~~~:
0.35 iii -+-5 turns ............. -_ ............ _-... ! ................................. :-_ .... _-..................... __ .1' .... __ •.......
iii ---*-4 turns 1 j j ! . i 1
0.3 0.3 0.4 '.5 0.6 0.7 0.8
Air Mass Flow Rate (kg/s)
Figure 4.7: Sensible Heat Ratio Resulting from Varying Expansion Valve Position and Evaporator Air Flow Rate
66
"-CD
== o C.
3.5
3
2.5
2
1.5
0.5
o
I I I
I I I i ·············o····o···@·1-9-·-9-··-9-···~···~..L~····~·· .. ~ ... @ .... ~.~.~ .... ~ ... ~ .... ~ .... @+~ ... ~ .................... -
::_x-I:~~::f::~~f::~:!:: o Compressor Power (Valve @ 7 turns) o Compressor Power (Valve @ 6 turns) <> Compressor Power (Valve @ 5 turns) x Compressor Power (Valve @ 4 turns) /::,. Air Pumping Power
···.·· ....... ·················r·······························N ote: The pressure drop across a typical
i amount of ductwork used in i . residential applications is included
······························-1.'································-1.[·············· in the air pumping power calculation.
. /::,. /::,.:6 6 A AiA A 6 6 /::"i6 6 6 6 6i/::" /::,. 6 i
I I I I
0.3 0.4 0.5 0.6 0.7 0.8
Air Mass Flow Rate (kg/s)
Figure 4.8: Compressor and Air Pumping Power Resulting from Varying Expansion Valve Position and Evaporator Air Flow Rate
67
4.1
4
I I I
J:I~~: __ ~~J::~~~hQ 3.9
10 0 0 0 010 0 0 0 1 1 0: : 0:0 0 :
: : : 0 0 : --tl---j---gto -: : : :
3.8
3.7
3.6
3.5
o 010 0 0 0 01 1 1 ..••......... ~ ............... j .........•...........•.. ·········r·~····o····o-···o········t··················· ............. j ............................... -
: : 0: 0 :
1 i 1 0 0 0 010 ; ······························r·······························[·······························r············· .... Expansion Valve Position
. x x x 1 x xli 1 0 7 turns ......•...•..............•••••. j ............... x····x···x··r")c··························t ·······························-1-· 0 6 turns
i i x x x xli 0 5 turns iii x x x 1 x 4 turns 1 i 1 X X1~"!"","" __ ,,,,
---r'r--[X 3.4 iii i
I I I I
0.3 0.4 0.5 0.6 0.7 0.8
Air Mass Flow Rate (kg/s)
Figure 4.9: System COP Resulting from Varying Expansion Valve Position and Evaporator Air Flow Rate
68
Analysis of COP Deeradation due to Expansion Valve Control
Results show that varying the expansion device opening provides control of total
system capacity. HQwever, the degradation of system COP that results from changing
capacity with the expansion valve is considerable. One way of detennining the significance
. of this degradation is to compare it to the COP degradation that occurs on a typical system
where capacity control is attained through on/off cycling. The details of such a comparison
are provided in the following paragraphs.
Three dimensionless terms are defined to help with the COP degradation
comparison: cycling efficiency, effective cycling efficiency, and duty factor. Cycling
efficiency applies to typical systems where capacity is controlled through system cycling.
It is defines as follows.
C I, Effi' COP during cycling yc mg IClency = rated system COP
(4.2)
Effective cycling efficiency applies to the system in this study where capacity is limited
through decreased expansion valve opening. Cycling efficiency and effective cycling
efficiency are equivalent quantities that can be directly compared.
Ef'" ' C l' Effi' throttled system COP lectlve yc mg IClency = ------=-----rated system COP
(4.3)
Duty factor applies to both systems in the comparison. It is a relative indication of the air
conditioning capacity required to meet the cooling load of a structure.
D F cooling load requirements uty actor = ---=---~---
rated system capacity (4.4)
The COP degradation comparison between a system that uses expansion device
opening to control capacity and a system that controls capacity through cycling is shown in
Figure 4.10. The solid line represents the cycling efficiency of an actual residential heat
pump installed in a typical residence [13]. The heat pump was instrumented to measure
compressor power along with air temperature, humidity, and flow rate. Measurements
were taken every second over one hour time intervals. Averaged capacity and power
values were used to calculate COP for the cycling system. Cycling efficiencies were
69
calculated with expression 4.2. Time averaged values of system capacity and the rated
capacity of the heat pump were used to calculate the duty factors of the cycling system
(expression 4.4).
The points below the typical cycling efficiency line on Figure 4.10 represent
predicted effective cycling efficiencies of a throttled system. Predicted capacity and power
measurements were obtained in facility mode for various expansion valve positions and
evaporator air flow rates (see Table 4.2). Throttled system COP was calculated using these
quantities. Rated system capacity and power were determined by simulating the system in
thermostatic expansion valve mode with 5 °C of evaporator superheat. These values were
used to calculate rated COP. Effective cycling efficiencies were calculated using expression
4.3, and duty factors were determined with equation 4.4.
The comparison shows that it is better from an efficiency standpoint to control
system capacity through on/off cycling than to use refrigerant throttling for capacity
control.
Control Simulation Results
• Effective air conditioner capacity control can be provided by adjusting the
opening of the expansion device.
• Sensible r~at ratio is moderately controllable through varying evaporator air
flow rate. In this study, sensible heat ratio rose from 0.48 to 0.58 as air flow
rate increased from 0.35 to 0.73 kg/so
• From an efficiency standpoint, it is better to control system capacity through
on/off cycling than to use refrigerant throttling for capacity control.
70
>o c Q)
'0 -iii Cl c '0 >()
Q)
> :;; o Q) -iii
0.95
0.9
0.85 0.65
o D I,'
i , , . iX , o
D
X
-rroriT~{~~~!;;[Hff~[:[f~;;~; o! ! X Air Flow Rate = 0.73 kg/s
~ 1
0.7 0.75 0.8 0.85 0.9 0.95
Duty Factor
Figure 4.10: Relative Magnitude of Effective Cycling Efficiencies
4.2.2 Compressor Speed and Evaporator Air Flow Rate Control
This section considers the ways that compressor speed and evaporator air flow rate
affect air conditioner performance. Table 4.3 summarizes the system loading conditions
and operating parameters that are considered in the study, and Figures 4.11 through 4.15
illustrate the simulation results. The following paragraphs discuss the air conditioner
capacity, sensible heat ratio, and system efficiency changes that result from controlling
compressor speed and evaporator air flow rate.
71
Table 4.3: System Loading Conditions and Operating Parameters
Loading and Operating Parameter Value(s)
Evaporator Air Mass Flow Rate 0.35 - 0.73 kg/s (2778 - 5794 lbmlhr) (0.02 kg/s increment)
Evaporator Inlet Air Temperature 28.3 °C (83.0 OF)
Evaporator Inlet Air Relative Humidity 62%
Evaporator Inlet Air Pressure 101.35 kPa (14.696 psia)
Evaporator Superheat 5.0°C (9 oF)
Compressor Speeds 2350,2900,3450 RPM
Condenser Inlet Pressure 1750 kPa (254 j>sia)
Subcooling 4.0°C (7.2 OF)
Discussion of Simulation Results
Compressor speed significantly affects system capacity. Figure 4.11 shows system
total and latent capacity as a function of compressor speed and evaporator air flow rate. As
compressor speed decreases, refrigerant mass flow rate drops, cauf'ing a corresponding
decrease in total capacity. In this study, a compressor speed decrease from 3450 to 2350
RPM results in a decrease in total capacity of approximately 25%. Figure 4.11 also
indicates that total evaporator capacity is a function of evaporator air flow rate. An increase
in evaporator air flow rate requires an increase in the expansion device opening to provide 5
°C of evaporator superheat. This results in a refrigerant mass flow rate increase and,
therefore, an increase in total system capacity.
Compressor speed and evaporator air flow rate have a fairly strong effect on
sensible heat ratio. This is illustrated in Figure 4.12 where sensible heat ratio is shown as a
function of compressor speed and evaporator air flow rate. This trend can be traced largely
to the evaporator temperatures that result from controlling these operating parameters.
Figure 4.13 shows the evaporator refrigerant inlet pressure at each compressor speed and
evaporator air flow rate combination. Since the evaporator inlet refrigerant is two phase,
these pressures provide an indication of evaporator temperature. Low sensible heat ratios
are observed for compressor speed and evaporator air flow rate combinations that produce
72
low evaporating pressures and, therefore, low evaporator temperatures. Conversely, high
sensible heat ratios correspond to conditions that produce relatively high evaporator
pressures.
System COP, as defined in expression 4.1, is a fairly strong function of
compressor speed. Figure 4.11 shows that system capacity decreases with reduced
compressor speed. Likewise, the compressor power decreases with compressor speed as
shown in Figure 4.14 where compressor and air pumping power are shown as a function ..
of compressor speed and evaporator air flow rate. Although these are competing effects in
terms of the COP calculation, significant COP gains are observed as compressor speed
decreases. This trend is illustrated in Figure 4.15 where COP is shown as a function of
compressor speed and evaporator air flow rate.
System COP is also affected by evaporator air flow rate as shown in Figure 4.15.
In the low to moderate range (approximately 0.35 to 0.53 kg/s), COP increases with air
flow rate as the resulting capacity gains overshadow the increases in compressor and air
pumping power. As flow rate continues to increase, however, the air pumping power
becomes increasingly significant causing system COP to decrease. The maximum COP
occurs at approximately 0.53 kg/s for the three compressor speeds considered.
Control Simulation Results
• Adjusting compressor speed is an effective way to control total system capacity.
In this study, a compressor speed decrease from 3450 to 2350 results in a
decrease in total capacity of approximately 25%.
• Varying evaporator air flow rate provides limited control of total system
capacity. Capacity control is most significant when the compressor is running
at its rated speed. In this case, variations in air mass flow rate from 0.35 to
0.73 kg/s result in a total capacity increase of over 15%.
• Sensible heat ratio is affected by compressor speed. In this study, as
compressor speed decreases from 3450 to 2350 RPM, sensible heat ratio
increases by 5 to 15% depending on evaporator air flow rate.
73
........ ~ ~
>. -·u as Co as ()
• Sensible heat ratio rises fairly linearly with increases in evaporator air flow rate.
In this study, sensible heat ratio increases of 20 to 30% resulted from increasing
evaporator air flow rate from 0.35 to 0.73 kg/so
• Limiting air conditioner capacity by decreasing compressor speed results in
increases in system COP. The system COP for a compressor speed of 2350
RPM is over 10% higher than the COP at 3450 RPM.
• System COP is maximized at moderate evaporator air flow rates for all
considered compressor speeds.
14
12
10
0 Latent @ 3450 RPM 0 Total @ 3450 RPM 0 Latent @ 2900 RPM
8 0 Total @ 2900 RPM <> Latent @ 2350 RPM 0 Total @ 2350 RPM
6
4
2 0.3 0.4 0.5 0.6 0.7 0.8
Air Mass Flow Rate (kg/s)
Figure 4.11: Total and Latent Capacity Resulting from Varying Compressor Speed and Evaporator Air Flow Rate
74
o :;:::; ca cr: .... ca G> :r G> :0 If) c:: G> en
0.7
0.65
0.6
0.55
0.5
0.45 o.~
i
1/-t::~rQ o
1 1 01 0 10 0 .............................. + ............................... + .................... -0-....... + ............................ D+ ............................. . I 1 0 0 I 0 0
1 1 10 10 0 10 0 1 01 01 0 01
............................... j ...................... ~ ........ ~ .............. B····~········+·······o···9 ............... + ............................. . , 0 '0 '0 ' , '0 0' , 10 0 01 0 1 1
0: 0: 0: i 0: 0 : 0 0 j Compressor Speed
·.···········Q .. ·····.··.····j.g..··q ..... ····o.··9 .. j ................................ +......... 0 3450 RPM ................. . 0 1 0 0 1 1
~ ~ % I I o 2900 RPM o 2350 RPM
0.4 0.5 0.6 0.7 0.8
Air Mass Flow Rate (kg/s)
Figure 4.12: Sensible Heat Ratio Resulting from Varying Compressor Speed and Evaporator Air Flow Rate
75
840
820
...... 800 al a.. ~ ....... Q) 780 ... :I I/) I/) Q)
760 ... a.. ... 0 -al 740 ... 0
---+------j~<>~o.r~---: : <>: D: D
............................. ..1 ........................ · ........ L. ...... ~ .... ~.··· .. · .... ·.·l..· ... ··.·.· .. B···Q ........ L ............................ . I I <> I D I I <>1 ID 10 0 , , D' 0' i <> i D i 0 i
·······························l···············~··············+·············0··············+··············0· ............ -t ............................. . i <> i D i 0 i I <> I D 10 I
.......................... .()..j ..................... 'Cj".Q .. l···············Q···O····?·f····· .. ········· .. ······ .. ······t .. ····················· .. ··· .. <> I D I 0 I I
I 10 I I <> i D oi i i
.. ······· .. ········· .. ····· .. ··1'0'·················0········t······························!················ .. ········· .. ···t····················· .. · .. · .. C-al > w 720
700
D D I 0 0 I I Compressor Speed ·············o···············!·o····························1····················· .. ·········t····· <> 2350 RPM ..................... .
01 i 1 D 2900RPM
-~OI---1-1 0 3450 RPM ..................... .
680 0.3 0.4 ".5 0.6 0.7 0.8
Air Mass Flow Rate (kg/s)
Figure 4.13: Evaporator Pressure Resulting from Varying Compressor Speed and Evaporator Air Flow Rate
76
"-CD ~ o
a..
3.5
3
2.5
2
1.5
0.5
o
l . OiO 0 0 0 0)0 0 i 00 0 Oi o 000 i i
............. 0 ... 0 ... .0.1.0 ............................ +·······························t····················· .......... -j-............................. .
ill ~ l lo 0 0 0 olD 0 0 0 OlD 0
............. [t .. H .. Q.i·Q .. ·g .. JL .. g .. ·~ .. f ................................ t .............................. --t-............................ . iii i
010 0 0 0 010 0 0 0 010 0 0 0 0 10 0
0 Compressor @ 3450 RPM 0 Compressor @ 2900 RPM 0 Compressor @ 2350 RPM 6 Air Pumping Power
····--------····---·.·---··.·--t·.·.·· .. ·····--··.···············f'······---------········-----···-:--·-------· ... _--- ... _-----------.; .. --_._-----------------_ .... _.
l l Note:The pressure drop across a typical 1 1 amount of ductwork used in
"""""""""""""",,·l ................................ ·f .............. residential applications is included I, :,i in the air pumping power calculation.
6 6 6 6'6 6 6 6 6i6 6
0.3 0.4 0.5 0.6 0.7 0.8
Air Mass Flow Rate (kg/s)
Figure 4.14: Compressor and Air Pumping Power Resulting from Varying Compressor Speed and Evaporator Air Flow Rate
77
4.8
4.6 ! 0 0 O!O 0 0 0 o!¢ 0 0 0 o!
.. ············o···~····O'·I··¢····~······················/································t·······························t·~····¢····················
I I I I 4.4
4.2
4
-:~IO-ooo-ojo--ODDOjD-DDD~k~ o I I I I
-I----~~:-:~J:~T----, 0' ,0 0,0 0
I 00 I . Comp~essor Speed I ···························o·j·O····························f······················· 0 3450 RPM ······1·······························
! ! 0 2900 RPM ! 00 I I o 2350 RPM I
3.8 ~ i 1
0.3 0.4 0.5 0.6 0.7 0.8
Mass Flow Rate of Air (kg/s)
Figure 4.15: System COP Resulting from Varying Compressor Speed and Evaporator Air Flow Rate
78
Chapter 5
Project Summary and Conclusions
A 3 ton split system air conditioner testing facility has been constructed to evaluate
air conditioner performance using zeotropic refrigerants. The facility consists of four main
parts: a split system refrigeration loop, an evaporator air loop, system measurement and
data acquisition equipment, and a gas chromatograph. The operator can easily control
system capacity and operating temperatures due to a variable speed compressor, a
condenser pressure controller, and an adjustable expansion device. The flexible evaporator
air loop provides dew point control to +1- 0.4 OF (+1- 0.2 °C), temperature control with an
accuracy of +1- 1 of (+1- 0.5 °C), and variable air flow rates up to 1750 CFM (830 LIs).
Accurate temperature, pressure, and flow rate data are taken throughout the facility and
stored by a user-friendly data acquisition system on a personal computer. A gas
chromatograph is used to accurately measure the mass composition of the refrigerant blend
in the refrigeration system.
A mathematical system simulation was developed to predict the performance of the
split system air conditioner testing facility charged with a zeotropic refrigerant consisting of
HFC-32, HFC-125, and HFC-134a (23%,25%, and 52% respectively). Descriptions of
each of the component models in the simulation are described along with a discussion of
the implementation of the component models in a Newton Raphson solver program.
Excellent system simulation performance is illustrated through graphical comparisons of
simulated and experimental results.
The mathematical system simulation was used to evaluate the performance and
control of split system air conditioners charged with a zeotropic refrigerant mixture of
HFC-32, HFC-125, and HFC-134a (23%,25%, and 52% respectively). First, the effects
of increasing the depth (number of rows) of the evaporator coil in a system were evaluated.
Comparisons show that improvements in system performance associated with increasingly
counterflow evaporator designs are overshadowed by other effects such as variations in air
side heat transfer coefficients.
Secondly, the controllability of a system charged with the zeotrope was evaluated.
In particular, changes in system capacity, sensible heat ratio, and system efficiency
resulting from controlling evaporator air flow rate, compressor speed, and expansion valve
79
opening were quantified. A summary of the main results of the system control study
follows.
• Although capacity control can be provided by adjusting the expansion device
opening, comparisons with published on/off cycling data show that it is better
from an efficiency standpoint to control system capacity with simple on/off
cycling.
• Efficient capacity control is attained through varying the compressor speed.
• Varying evaporator air flow rate is an effective way to control system sensible
heat ratio.
80
List of References
·1 Barnett, C. J., "HVAC Professor Learns CFC-ozone Theory Firsthand," Air
Conditioning, Heating and Refrigeration News, May 16, 1994.
2 "Standard Methods for Laboratory Airflow Measurement," ASHRAE Standard,
ANSII ASHRAE 41.2-1987 (RA 92).
3 Darr, J. H. and Crawford, R. R., "Modeling of an Automotive Air Conditioning
Compressor Based on Experimental Data," ACRC Technical Report, University
of lllinois at Urbana-Champaign, 1992.
4 Martin, D. L., "Digital Computer Simulation of Water-Source Heat Pump
Performance," Master's Thesis, University of lllinois at Urbana-Champaign,
1981.
5 Ragazzi, F., "Thermodynamic Optimization of Evaporators with Zeotropic
Refrigerant Mixtures," Ph.D. Thesis, University of Illinois at Urbana
Champaign, 1995.
6 Paliwoda, A., "Generalized Method of Pressure Drop and Tube Length Calculation
with Boiling and Condensing Refrigerants Within the Entire Zone of Saturation,"
International Journal of Refrigeration, Vol. 12, November 1989, pp.314-322.
7 Paliwoda, A., "Generalized Method of Pressure Drop Calculation Across Pipe
Components Containing Two-Phase Flow of Refrigerants," International Journal
of Refrigeration, Vol. 15, No.2, 1992, pp. 119-125.
8 Stoecker, W. F., and Jones, J. W., Refrigeration and Air Conditioning, Chapter
13, McGraw-Hill, New York, 1982.
81
9 Gallagher, J., McLinden, M., Morrison, G., and Huber, M., "NIST
Thermodynamic Properties of Refrigerants and Refrigerant Mixtures - Version
4.0," National Institute of Standards and Technology, 1993.
10 Ragazzi, F. and Nygaard, T. R., "Refrigerant Properties for Pure and Mixed
Refrigerants: An Interpolation Subroutine Package," ACRC Technical
Memorandum #16, University of illinois at Urbana-Champaign, 1995.
11 Stoecker, W. F., Design of Thermal Systems, Third Edition, Chapter 6, McGraw-
Hill, New York, 1989.
12 Mullen, C. E., "Room Air Conditioner System Modeling," Master's Thesis,
University of illinois at Urbana-Champaign, 1994.
13 Zietlow, D. c., "Performance Evaluation of Air to Air Heat Pumps," Master's
Thesis, Bradley University, 1988.
82
Appendix A
Wiring Schematics
83
00 .j:::..
240 VAC
- Remote - Low Level I'" Unit On/Off Cntrl. Sw.
(located on control panel)
24 VDCt--U Power 1 Supply T
R21
T Inverter Start Contact
Figure A.I: Compressor Control Schematic
Rl
LS
Legend
LSl
Rl
R2
R2~
Compressor~ Heater$
High Pressure Cut-ou~
Low Pressure Cut-out
R
Liquid Line Solenoid Valve
LS 1 Control Relay
Compressor Start Relay -- -----
it
00 Ul
240 VAC 3 Phase
24VAC
PIO Control Signal (from cntrl. panel)
Air Proving Switch High Temp. CUtout (Adjustable)
240 VAC 1 Phase
SCR Htr. Controlle
C2
Figure A.2: Heater Control Schematic
Cl
Rl f Overtemp. Sw Htr. On/Off (Cntrl. Panel)
CUll TT
Air Proving Switch
"Heaters Disabled" Indicator Lamp
240 VAC 1 Phase 5.8 kW Heater
240 VAC 3 Phase 5.5 kW Heater
110 VAC 60 Hz (from cntrl. panel)
Legend
Cl
C2
Rl
1 Htr. On/Off I (Cntrl. Panel)
Rl
11 TT
5.5 kW Heater Contactor
5.8 kW Heater Contactor
Heater Disable Relay
Appendix B
Data Acquisition Terminal Panel Connections
Terminal Panel #1 Channels 1-8 16 bit resolution
Channel Number Measurement
1 Unused
2 Temperature Reference - Panel #1
3 Evaporator Air Inlet Temperature
4 Evaporator Air Inlet Temperature
5 Evaporator Air Inlet Temperature
6 Evaporator Air Inlet Temperature
7 Evaporator Air Inlet Temperature
8 Evaporator Air Inlet Temperature
Terminal Panel #2 Channels 9-16 16 bit resolution
Channel Number Measurement
9 Evaporator Air Inlet Temperature
10 Temperature Reference - Panel #2
11 Evaporator Air Outlet Temperature
12 Evaporator Air Outlet Temperature
13 Evaporator Air Outlet Temperature
14 Evaporator Air Outlet Temperature
15 Evaporator Air Outlet Temperature
16 Evaporator Air Outlet Temperature
86
Terminal Panel #3 Channels 17-24 12 bit resolution
Channel Number Measurement
17 Evaporator Return Bend Temperature
18 Evaporator Return Bend Temperature
19 Temperature Reference - Panel #3
20 . Evaporator Return Bend Temperature
21 Evaporator Return Bend Temperature
22 Evaporator Return Bend Temperature
23 Evaporator Return Bend Temperature
24 Evaporator Return Bend Temperature
Terminal Panel #4 Channels 25-32 12 bit resolution
Channel Number Measurement
25 Evaporator Return Bend Temperature
·26 Evaporator Return Bend Temperature
27 Tem})erature Reference - Panel #4
28 Evaporator RetUrn. Bend Temperature
29 Evaporator Return Bend Temperature
30 Evaporator Return Bend Temperature
31 Evaporator Return Bend Temperature
32 Evaporator Return Bend Temperature
87
Terminal Panel #5 Channels 33-40 12 bit resolution
Channel Number Measurement
33 Evaporator Air Outlet Temperature
34 Evaporator Air Outlet Tem~rature
35 Evaporator Air Outlet Temperature
36 Temperature Reference - Panel #5 .
37 Evaporator Air Outlet Temperature
(after blender)
38 Evaporator Air Outlet Temperature
(after blender)
39 Air Temperature - Nozzle Station
40 Unused
Terminal Panel #6 Channels 41-48 12 bit resolution
Channel Number Measurement
41 Evaporator Refrigerant Outlet Temp.
(in flow)
42 Evaporator Refrigerant Outlet Temp.
(surface)
43 Oil Sel'arator Outlet Refrigerant Temp.
44 Temperature Reference - Panel #6
45 Exp. Valve Inlet Refrigerant Temp.
(surface)
46 Exp. Valve Inlet Refrigerant Temp.
(in flow)
47 Subcooler Outlet Temperature
48 Compressor Inlet Temperature
88
Terminal Panel #7 Channels 49-56 16 bit resolution
Channel Number Measurement
49 Evaporator Air Outleti Atm. Pressure
50 Nozzle Air Differential Pressure
51 Unused
52 Nozzle Air Outleti Atm. Pressure
53 Evaporator Air Inlet Dew Point
54 Unused
55 Evaporator Air Outlet Dew Point
56 Evaporator Air Differential Pressure
Terminal Panel #8 Channels 57-64 16 bit resolution
Channel Number Measurement
57 Compressor Power
58 Refrigerant Flow Rate
59 Evaporator Ref. Differential Pressure
60 Evaporator Refrigerant Inlet Pressure
61 Exp. Valve Refrigerant Inlet Pressure
62 Compressor Refrigerant Inlet Pressure
63 CondenserlSubcooler Dif. Pressure
64 Condenser Refrigerant Inlet Pressure
89
Appendix C
Facility Operation
The following appendix contains start-up and shutdown procedures for the . evaporator testing facility. It may be helpful to review the main system controls shown in
figure C.l before operating the unit.
Facility Startup Instructions
1 Ensure that power is applied to all components.
2 Make sure condenserlsubcooler water valve is open. The valve is located on the
east wall of the laboratory.
3 Open the needle valve located above the subcooler on the condensing unit
approximately two turns to allow a small amount of water to flow through the
subcooler (see Figure 2.3). This ensures that subcooled refrigerant liquid will
enter the ma"~ flow meter during system operation for accurate measurements.
4 Apply power to pressure transducers, power supplies, mass flow meter, and dew
point sensors using the power supply I transducer power switch located on the main
control panel (see switch #9 on figure C.l).
5 Initiate air flow using blower On/Off switch (see switch #5 on figure C.l).
6 Adjust air flow rate using blower speed potentiometer (see potentiometer #6 on
figure C.l). Use nozzle station pressure drop (display Strawberry Tree channel 50)
to determine actual flow rate if necessary. Section 2.2.2 provides a relationship
between nozzle station pressure drop and air flow rate.
90
1 Humidifier On/Off Switch
2 PID Humidity Controller
3 Trim Heater On/Off Switch (0 - 5.8 kW)
4 PID Temperature Controller
5 Blower On/Off Switch
6 Blower Speed Potentiometer
7 Baseline Heater On/Off Switch (5.5 kW)
8 "Heaters Disabled" Indicator
9 Power Supply / Transducer Power Switch
10 Refrigeration System On/Off Switch
11 Compressor Speed Potentiometer
Figure C.I: Experimental Facility Control Panel
91
7 Each dew point sensor is equipped with a rotameter for measuring the air sampling
rate. Using the valves located on the two rotameters, adjust the air flow through.
each of the dew point sensors to approximately 2.5 cubic feet per hour.
8 Tum on compressor using refrigeration system OnlOff switch (see switch #10 on
figure C.l).
9 Tum on the baseline and trim heaters using the heater OnlOff switches (see switch
#3 and #7 on figure C.l).
10 Adjust evaporator air inlet temperature setpoint using the arrow keys on the Omega
PID controller (see controller #4 on figure C.l).
The following three steps should be followed if and only if humidity
control is required.
11 Enable the humidifier using the humidifier OnlOffSwitch (see switch #1 on figure
C.l).
12 Verify that the dew point indication on the Honeywell PID c "l1troller (#2 on figure
C.l) is the same as that displayed on the evaporator inlet dew point sensor
controller. It may be necessary to wait a few minutes for the dew point sensor
controller to begin supplying a dew point measurement.
13 Set desired dew point using the arrow keys on the Honeywell PID controller. If the
humidifier is cold, allow approximately 20-30 minutes for the air humidity control
process to begin.
92
Special Notes:
Compressor spetXi is adjustable using the potentiometer located on the main control
panel (see potentiometer #11 on figure C.1). Warning!!! Operation of the
compressor below 40 Hz could result in poor compressor lubrication
and premature compressor failure.· The compressor input frequency is
displayed on the compressor variable speed drive located on the south wall of the
laboratory.
The manually adjustable expansion device is located in the liquid line near the
evaporator test section. Counter-clockwise rotation of the vernier valve handle
opens the expansion valve.
A mechanical, proportional controller mounted on the condenser water line allows
the operator to adjust the system's condenser pressure (see Figure 2.3). Counter
clockwise adjustment of the controller increases the condensing pressure.
Conversely, clockwise adjustment decreases the pressure. A pressure gage
mounted near the controller helps the operator to properly adjust the desired
condenser pressure.
Facility Shutdown Instructions
1 If humidity control was used, turn off humidifier using humidifier On/Off switch
located on main control panel.
2 Tum off baseline heater, trim heater, and refrigeration system control switches.
3 When compressor stops, turn off blower using the blower OnIOff switch located on
the main control panel.
4 Shut off power supply I transducer power switch located on main control panel.
5 Close subcooler water control valve located above the subcooler on the condensing
unit.
93
Appendix D
Inverter Output Power Measurement Uncertainty
An AC, variable speed motor drive controls motor speed by altering the frequency
of the signal which drives an electric motor. The speed control does this in two steps.
First, input AC power is converted to DC in a rectification stage. Then, through modem
solid state switching techniques, the speed control reconstructs an AC signal at a frequency
which corresponds to a desired motor speed.
The AC signal produced by a variable frequency drive is sufficient for the purposes
of running an electric motor. However, the driving signal is very noisy. Since most watt
transducers are designed to measure power at a narrow band of frequencies near 60 Hz, it
is important to consider the possibility of "unseen" power delivery at secondary frequencies
(noise). The purpose of this study is to take a closer look at the reconstructed signals of a
variable speed drive in hopes of quantifying the power delivered at subordinate
frequencies.
Hardware
Calculation of the actual drive output power measurement requires the evaluation of
both the signal voltage supplied to the motor as well as the resulting motor current. In
addition, these signals must be properly conditioned for input to an HP 3652 signal
analyzer. The following paragraphs describe the methods used to provide the conditioned
voltage and current measurements. An illustration of the current and voltage conditioning
circuitry appears in Figure D.l.
Current Measurement
Shunts are used to evaluate the current running in each of the three signal phases.
A shunt is a very small, well-known resistance placed in series with each phase. As
current passes through the shunt, a voltage drop results which is proportional to the phase
94
current. The shunts used in this study provide a 100 millivolt drop for 15 Amps of phase
current.
The voltage drop provided across each shunt must be amplified and isolated before
it is connected to the signal analyzer. Both amplification and isolation are provided by an
Analog Devices AD-2IOAN isolation amplifier.
Voltage Measurement
Differential voltage measurements are made between each of the three signal
phases. These line-to-line measurements are first attenuated by a voltage divider to a
magnitude similar to those measured across the shunts. A second Analog Devices AD-
210AN isolation amplifier is used to provide signal gain and isolation. The current and
voltage isolation amplifiers are intentionally configured with the same gain to minimize the
differences between their respective frequency responses.
Experimental Method
The isolated and conditioned current and voltage signals described previously are
connected directly to an HP 3652 Dynamic Signal Analyzer. The analyzer provides an
average RMS current and voltage measurement at each of the frequencies contained in the
input signals. In, 'dition, the analyzer can compute the phase relationship between the
current and voltage signals at each frequency. Examples of the analyzer outputs appear in
Figures D.2, D.3, and D.4. The power delivered at subordinate frequencies can then be
expressed as a percentage of the power delivered at the operating frequency as shown
below.
Power at nOIse frequencies P - x 100
relative - Power at desired operating frequency
where:
_ LV noiseInoise cos( S nOise)
- V opIop COS( S op ) x 100
P relative == Relative Magnitude of Power delivered at Secondary Freqs.
V,I,Snoise == Voltage, Current, and Phase Angle at noise frequencies
V,I,Sop == Operating Frequency Voltage, Current, and Phase Angle
95
(D.I)
Line 1
Line 2
Line 3
Vl
V2
V3
~1'
\'22'
V33'
-------~~t\I\VV~l-'--------------------
________ ~_~-2-'----------------------________ V3 __ ~~3-'----------------------
~ Ammeter Shunt (3)
=1 1 ~I K
1 -[3Jc> Voltage Control Switch Attenuation Amplification / Isolation
Connection to Compressor
., To Analyzer
3 Positions Provide Analog Devices AD-21 OAN
~2, \'23, orV13
:1 1 .[3Jc> • To Analyzer
Current Control Switch Amplification / Isolation
3 Positions Provide Analog Devices AD-21 OAN
Vll', V22', or V33'
Figure D.l: Variable Speed Drive Voltage I Current Conditioning Circuitry
96
Results
The relative amount of power delivered at secondary frequencie~ increases as the
operating frequency deviates from 60 Hz as indicated below:
RESULTS
Operating Frequency Relative Power Delivered at Secondary Frequencies
60.0 Hz. 1.12%
47.5 Hz. 2.40%
41.2 Hz. 4.32%
As shown in the results table, variable speed drive output power measurement
uncertainties can be significant if the measuring device used is incapable of considering
power delivered at all frequencies; especially when the drive's operating frequency is below
60 Hz.
97
Illverter Frequency = 41.2 Hz
Vohagt.
Curtent
,Phase Angle
X--41.e Hz Ve-4.22912 v
Pg~~?~~~-'-'T"- 500:..:::;A,-,V4'P'--_0",,?,;::;0=v ~ HjP1_-,.. ............... _;-: Meg f-....... -.-.-~- [' - I -t- i r~ I V I
.--!H-~-+--.. _+--!_--+ .... - .. __+--+_-_+_-........;
0.0
POWE 3.2
Meg
R
10
SPEC2 !500Ava
! rme V
f--t----+-.. ----r , ... 1
i i
0.0 II .1. J 10
X-41.e Hz Ve--4.0174 Oeg
lU
! I !
! i j ;
0"0'1111 Henn
I j : , , ;
Hz
F~~g ,fIgs~ __ . ___ ...... , ....... _ .. 500AV~.. O~OV ~ ...... He?n k. . '" .!
/Oiv. f : .. ..... _ ...... _ ..... __ ._ .. _.-: - .. -:-.. ---+--
Oeg
, I , I I
!5.01k.
---............. ---. + ... --+--, ......... ..l-,--~f4-- .... ; ...... ------;...-.-.. i ,.
-2.0! :: i k ... 1"o_......:---L.- ... _-' --... .LHt---...... ~ .. -.-~-'- ···· .... s:oTk
f
Figure D.2: Variable Speed Drive Output Voltage, Current, and Phase Angle at 41.2 Hz
98
Iovcrccr Frequency = 47.5 Hz
Voltage
Current
PhaSe Angle
X-S.87S5kHz Y.-4S.7 ... semv Pg~~F' SPEC-50
Mao
rma V
0.0
POWE 3.S
Mag
rom. V
0.0
10
R SPECS
;
I
.- :. I. .I 10
X-"'7.5 Hz Y.--.... 9S:1.3 O.g
FREQ RESP 400
0lll:OV1e ! . i
500Ava 0"'0'111: Han"
I 1 , ;
I I I i 1 ,
I I , ; ;
f I
t !
l~ i I l , :
Hz 5.05ok
__ ..:;5r=0:..::0:;..::A::.V:"~1"-...-;0~lII:=0.:.V.:::l.lL....':"'.~ __ . _____ .... ! I' i" ; i !
200 r··---~------4'''--+--~------i-t ,~-..-;.---"---
/01v.· ~-+ ____ ~ __ ~~_~ __ ~ ________ ~ ___ ~ ___ ~ __ ~
Oeg
Figure D.3: Variable Speed Drive Output Voltage, Current, and Phase Angle at 47.5 Hz
99
Inverter Frequency = 60 Hz
Voltage
Current
Phase AnBle
x-so Hz Ye-a .33503 .V
P~~~I SP~~_. 100AVr O!\:Ovlp Henn
Meg
rm. V
0.0
POWE 3.2
Meg
rme V
R
1 I
I !
1
10
SPEC2
I I i ! : j i , -i I , ! ... j, .t 0.0
:to
x-so Hz Ya--1.9S01 Oeg
1300Ava Olll;Ovl Hen"
1
I . •
! I
I ! I
, ! Hz 15.011<
F:gg i RES~ ___ '_"-_-=;1Q9AVP 0r'ovlB He?n _
__ +-'-4 __ ~; ___ ~ __ ~i __ ~ ____ ~ 400
/Oiv
Phase
Deg
: ' ,~",~do.-_, __ .,.",~ __ ' _ ..• ___ -..J
5.01k
Figure D.4: Variable Speed Drive Output Voltage, Current, and Phase Angle at 60.0 Hz
100
Appendix E
List of Component Manufacturers
Device Manufacturer Model Number
Compressor Copeland CRG3-02S0-TFS
Compressor Var. Spd. Drive Asea Brown Boveri M01712AOO
Power Transducer Ohio Semitronics, Inc. GWS-023CXS
Oil Separator Temprite 922
Condenser Refrigeration Research, Inc. S026-S
Ref. Mass Flow Meter Micro Motion, Inc. DS02SS119
Ref. Mass Flow Transmitter Micro Motion, Inc. RFT97121PNU
Expansion Valve Hoke 2334F4B
Evaporator Colmac Coil Mfg., Inc. DXL-24x24-4R-9F-WR-R/L
Ref. Gage Pressure Sensors Setra 207
Ref. Dif. Pressure Sensors Setra 22S-1
Blower Dayton 3C106A
Blower Var. Spd. Drive IDMContn 3, Inc. CIMR -7 .5G2. E-1O
Air Pressure Transducers Setra 264
Air Heater Indeeco GUA 00S.50 020.000x020.000
PID Heater Controller Omega CN2001T-FI-DI-AM-A
SCR Heater Controller Omega SCR71Z-230
Humidifier Pure Humidifier Company PS-S.S (S)
Water Preheater US Craftmaster EIE2.SUS
PID Humidity Controller Honeywell DC3002-0-01A-2-00-0111
Evap Inlet Dew Pt. Sensor General Eastern Ml/1111H
Evap Outlet Dew Pt. Sensor General Eastern M2 / D2 / T-l00
Data Acquisition Computer Apple Mac II
Data Acquisition Hardware Strawberry Tree Comp., Inc. ACM2-12, ACM2-16
Gas Chromatograph Gow-Mac Instrument Co. SSO
GC Integrator Hewlett Packard 339S
101
Appendix F
Selected System Model Source Code
EQNS.f
C**********************************************************************
Subroutine CalcR(VariableNum,R)
C********************************************************************** C C C C C C C t C C C C C C C C C C C C C C C C C C C C C C C C C C
PURPOSE: Calculate the values of the residual equations. A model's governing equations are converted into residual format according to the following example: Eqn #1 : LHS = RHS ---> R(l) =RHS - LHS
Where LHS and RHS are the left-hand and right-hand sides of the equation respectively. The equation is considered solved when the residual value is equal to zero within a specified tolerance.
CalcR is called repeatedly by CalcD (Jacobian matrix calculation) and is called by NRMethod once per Newton-R ..,hson iteration.
INPUTS: VariableNum - current variable number If VariableNum=O, all of the residual values are to be
determined at once. Otherwise, VariableNum represents the variable with respect to which the partial derivatives are being taken.
SHARED IN COMMON BLOCKS: NonZeroList -list of nonzero elements of the Jacobian to
facilitate sparse-matrix Jacobian calculation. Column #n of NonZeroList contains a list of all of the residual equations that contain variable #no Column #0 of NonZeroList contains a list of ALL residual equations and is used when all of the residual values are to be determined at once.
NonZeroFlag - this flag is set .true. only when the NonZeroList is being built. This information is needed when a particular residual equation does not always show its dependence on all of the variables that it may contain, e.g.
102
C when certain equations may be switched during the course of C a solution or a function such as 'max' or 'min' is used. C The Jacobian that is calculated during building the C NonZeroList is not used for any calculations, thus it does C not to be the true Jacobian, but it must be non-zero C EVERYWHEl,rn that the true Jacobian will EVER be non-zero. C XK - the array of variable and parameter values C All variable and parameters - these are included in EQUlVLNT.INC C and are made equivalent to XK array elements via the C 'Equivalence' statement C C OUTPUT C R - the array of residual values C C********************************************************************** *
Implicit None
Include 'DIMENSN.INC' Integer VariableNum
Double Precision R(Xmax) Double Precision A_condenser, A_disttube, A_expvalve Double Precision A_LiqLine, B_condenser, B_disttube Double Precision C_compl, C_comp2, C_comp3 Double Precision C_expvalve, diamH_condenser, Displacement Double Precision dP _condenser, dP _condvapor, dP _disttube Double Precision dP _distvapor, dP _expvalve, dP _LiqLine Double Precision dT_superheaCref, dummy, d_disttube Double Precision Ccondenser, Cdisttube, G_condenser Double Precision G_disttube, G_expvalve, G_LiqLine Double Precision Liquid_Viscosity, L_condenser, L_disttube Double Precision mdotref, mdoCref, Perimeteccond Double Precision P _disttube_in, P _refevap_out, Re_condenser Double Precision Re_disttube, Specvol_suction, Theta_condenser Double Precision Theta_disttube, T_condenser_in, T_disttube_in Double Precision T_LiqLine_in, T_satliq_in, Vapoc Viscosity Double Precision Vdotref, Volumetric_Efficiency, V _condliquid Double Precision V _condvapor, V _expvalve_in, V _LiqLine Double Precision V _tubeliquid, V _tubevapor, x_disttube
Logical Range, diCinlecconditions
Include 'seg.inc' Include 'hx.inc' Include 'refprop.inc'
C *** EQUIVLNT.INC declares all the variables and parameters and C *** sets them to be equivalent to elements of the XK array.
Include 'EQUIVLNT.INC'
zero = 0.0 unity = 1.0
103
C************************************* C ****** GOVERNING EQUATIONS ****** C*************************************
C *** Condenser Pressure Drop ***
C X_sectional Area of Refrigerant Passage in Condenser [mA2] A_condenser = 3.14159*0.0006452/4*((1 **2) - (0.614**2))
C Wetted Perimeter [m] Perimeteccond = 3.14159*(1+0.614)*0.0254
C Hydraulic Diameter of Condenser [m] diamH_condenser = 4* A_condenserlPerimeteccond
C Length of Condenser Tubing [m] L_condenser = (3.14159*11)*5.5*0.0254
C Condenser Mass Flux [kg/s.mA2] G_condenser = mdoCrefrigeranti A_condenser
C Saturated Vapor Specific Volume [kg/mA3] C Saturated Liquid Specific Volume [kg/mA3]
Call SaturationInt(reCprint,(P _condensecin*14.6961101.35) * ,dummy ,dummy, V _condvapor, V _condliquid,dummy * ,dummy, dummy, dummy, dummy) V _condvapor = V _condvapor * 0.062428 V _condliquid = V _condliquid * 0.062428
C Vapor Reynolds Number in Condenser Call TsatPInt(reCprint,(P _condensecin*14.6961101.35) * , T_condensecin, dummy) Call Viscosity( unity, T _condensecin, Vapoc Viscosity) Vapor_Viscosity = Vapoc Viscosity * 4. 1337e-4 Re_condenser = G_condenser*diamH_condenserNapor_ Viscosity
C Single Phase Friction Coeficient Ccondenser = 470*Re_condenser**( -0.480)
C Pressure Drop - Condenser Saturated Vapor [Pa] dP _condvapor = Ccondenser*L_condenser*(G_condenser**2)*V _condvapor * 1(2*diamH_condenser)
C Liquid 1 Vapor Gradient Ratio [dimensionless] Call TsatPInt(reCprint,(P _condensecin*14.6961101.35) * , dummy, T_condenser_in) Call Viscosity(zero,T_condensecin,Liquid_ Viscosity) Liquid_Viscosity = Liquid_Viscosity * 4. 1337e-4 Theta_condenser = (V _condliquidN _condvapor)* * (Liquid_ ViscosityNapor_ Viscosity)**(0.25)
C Two-Phase Flow Factor [dimensionless]
104
B_condenser = 0.36*(Theta_condenser+ 1)
C Condenser Pressure Drop - Two Phase [kPa] dP _condenser = dP _condvapor*B_condenser/1000
C *** Liquid Line Pressure Drop ***
C Liquid Line Inlet Pressure [kPa] P _LiqLine_in = P _condensecin - dP _condenser
C Liquid Line Inlet Specific Volume [mJ\3/kg] C Liquid Line Inlet Temperature [OC]
Call SaturationInt(reCprint,(P _LiqLine_in* 14.696/1 0 1.35) * ,dummy,T _satliq_in,dummy,V _LiqLine,dummy * ,dummy, dummy, dummy, dummy) V _LiqLine = V _LiqLine * 0.062428 T_LiqLine_in = (T_satliq_in-32)*5/9 - dT_subcool
C X_sectional Area of Liquid Line [mJ\2] A_LiqLine = 3.14159*.0006452*(0.43**2)/4
C Liquid Line Mass Flux [kg/s.mJ\2] G_LiqLine = mdocrefrigerantl A_LiqLine
C Liquid Line Pressure Drop [kPa] dP _LiqLine = 65. 166*(G_LiqLine**2)*V _LiqLine/2oo0
C *** Expansion Valve Equations ***
C Expansion Valve Inlet Pressure [kPa] P _expvalve_in P _LiqLine_in - dP _LiqLine
C Expansion Valve Inlet Specific Volume [mJ\3/kg] Call SaturationInt(reCprint,(P _expvalve_in* 14.696/10 1.35) * ,dummy,dummy,dummy,V _expvalve_in,dummy * ,dummy,dummy,dummy,dummy) V _expvalve_in = V _expvalve_in * 0.062428
C X_sectional Area of Nominal Valve Orifice [mJ\2] A_expvalve = 3.14159* .0006452*(0.125**2)/4
C Expansion Valve Mass Flux [kg/s.mJ\2] G_expvalve = mdoCrefrigerantlA_expvalve
C Expansion Device Flow Coeficient C_expvalve = 429.85*exp(Valve_Position*(-0.684))+18.32
C Expansion Valve Pressure Drop [kPa] dP _expvalve = C_expvalve*(G_expvalve**2)*V _expvalve_inl2000
C *** Distributor Tube Pressure Drop ***
105
C Distributor Tubing Inlet Pressure [kPa] P _disttube_in = P _expvalve_in - dP _expvalve
C Distributor Tube Diameter [m] d_disttube = 0.15 *0.0254
C X_sectional Area of Distributor Tube [m"2] A_disttube = 3. 14159/4*(d_disttube**2)
C Length of Distributor Tubing [m] L_disttube = 18*0.0254
C Distributor Tube Mass Flux [kgls.m"2] G_disttube = mdocrefrigerantl(A_disttube*2)
C Saturated Vapor Specific Volume [kg/m"3] C Saturated Liquid Specific Volume [kglm"3]
Call SaturationInt(reCprint,(P _disttube_in* 14.696/1 0 1.35) * ,dummy,dummy,V _tubevapor,V _tubeliquid,dummy * ,dummy, dummy, dummy, dummy) V _tubevapor = V _tubevapor * 0.062428 V _tubeliquid = V _tubeliquid * 0.062428
C Vapor Reynolds Number in Distributor Tube . Call TsatPInt(reCprint,(P _disttube_in*14.696/101.35) * , T_disttube_in, dummy) Call Viscosity(unity,T_disttube_in,Vapor_ Viscosity) Vapoc Viscosity = Vapor_Viscosity * 4. 1337e-4 Re_disttube = G_disttube*d_disttubeNapoc Viscosity
C Single Phase Friction Coeficient Cdisttube = 0.3164*Re_disttube**(-0.: 'i0)
C Pressure Drop - Distributor Tube Saturated Vapor dP _distvapor = Cdisttube*L_disttube*(G_disttube**2) * *V _tubevapor/(2* d_disttube)
C Liquid I Vapor Gradient Ratio [dimensionless] Call TsatPInt(reCprint,(P _disttube_in* 14.696/1 0 1.35) * ,dummy, T_disttube_in) Call Viscosity(zero,T_disttube_in,Liquid_ Viscosity) Liquid_Viscosity = Liquid_Viscosity * 4. 1337e-4 Theta_disttube = (V _tubeliquid/V _tubevapor)* * (Liquid_ ViscosityNapor_ Viscosity)**(0.25)
C Expansion Valve Enthalpy [kJ/kg] C Distributor Tube Quality
Call HPTInt(reCprint,(P _LiqLine_in*14.696/101.35) * ,(T_LiqLine_in*915 + 32),h_expansionvalve,range) Call XPHInt(reCprint,(P _disttube_in* 14.696/1 0 1.35),
* h_expansionvalve, x_disttube, range) h_expansionvalve = h_expansionvalve * 2.3244
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C Two-Phase Flow Factor [dimensionless] B_disttube = (Theta_disttube+2*(1-Theta_disttube)*x_disttube) * *( 1-x_disttube )**(0.33333)+x_disttube**3
C Distributor Tube Pressure Drop - Two Phase [kPa] dP _disttube = dP _di~tvapor * B_disttubellOOO
C Evaporator Inlet Pressure [kPa] P _refevap_in = P _disttube_in - dP _disttube
C *** Evaporator Equations ***
diCinlecconditions = * (testinput_mod( testnum, 1 ).ne.h_expansionvalve/2.3244 ).or. * (testinpuCmod(testnum,2).ne.P _refevap_in*14.6961l01.35).or. * (testinpucmod(testnum,3).ne.T_airevap_in*915 + 32).or. * (testinpuCmod(testnum,4 ).ne.P _airevap_in* 14.696/10 1.35).or. * (testinpuCmod(testnum,5).ne.relhum_in).or. * (testinpuc mod(testnum,6).ne.mdoCrefrigerant*7936.64).or. * (testinpucmod(testnum, 7).ne.mdotair*7936.64)
if (diCinleCconditions) then
print * ,'Calling Model'
testinpuCmod(testnum, I) = h_expansionvalve/2.3244 testinpuCmod(testnum,2) = P _refevap_in*14.696/101.35 testinpucmod(testnum,3) = T_airevap_in*915 + 32 testinpucmod(testnum,4) = P _airevap_in*14.696/101.35 testinpucmod(testnum,5) = relhum_in testinpucmod(testnum,6) = mdoCrefrigerant*7936.64 testinpucmod(testnum,7) = mdotair*7936.64
Call hx_init Call hx_soln Call hx_fmlanl
endif
P _refevap_out = testoutpuCmod(testnum,29)*101.351l4.696 h_suction = testoutpucmod(testnum,30)*2.3244
dT _superheacref = 10
R(1) = (dT_superheat - testoutpuCmod(testnum,32)*519) 1 dT_superheacref
C ***Compressor Model Equations***
C_compl = -0.062225 C_comp2 = -0.104112 C_comp3 = 1.094268
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C Compressor Suction Pressure P _suction = P _refevap_out
C Compressor Displacement [cmA3] Displacement = 60.632
C Compressor Efficiellcies Volumetric_Efficiency = C_comp2 * P _condensecinIP _suction * + C_compl * CompressocSpeed/3450 + C_comp3
C Compressor Suction Specific Volume [mA3/kg] Call TPHiter(reCprint,(P _suction * 14.6961101.35) * ,(h_suctionl2.3244),T_suction) Call VPTInt(reCprint,(P _suction* 14.69611 0 1.35), T _suction * ,spec Vol_suction,Range) T_suction = (T_suction-32)*519 SpecVoCsuction = SpecVoCsuction * 0.062428
C Compressor Volumetric Flow Rate [mA 3/s] V dotref = Volumetric_Efficiency*Compressor_Speed*Displacementl( le6*60)
C Refrigerant Mass Flow Rate [kgls] mdoCref = 0.06
R(2) = (mdocrefrigerant - VdotreflSpecVoCsuction)/mdoCref
Return End
CHECKMOD.f
C********************************************************************** Subroutine IC
C PURPOSE - The IC (Initial Check) routine for the model may be C used for pre-processing of variable initial guesses or C parameter values, checking XK values and setting equation C flags accordingly, or performing any other model-specific C operations before the start of the Newton-Raphson solution C process.
Implicit None
Return End
C********************************************************************** Subroutine BC(AbortStep,Switch)
C PURPOSE - The BC (BoUndary Check) routine for the model may be
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C used to check variable values and ensure that they fall C within certain boundaries. The BC subroutine is also C intended to facilitate switching of equations in C mid-solution. Based on the variable values, logical flags C may be set that "switch" model equations in or out.
Implicit None
Return End
C********************************************************************** Subroutine FC
C PURPOSE - The FC (Final Check) routine for the model may be C used for post-processing of variable or parameter values, C checking XK values and setting equation flags accordingly, C or performing any other model-specific operations after the C Newton-Raphson solution is complete.
IMPLICIT NONE
Include 'seg.inc' Include 'hx.inc' Include 'EQUIVLNT.INC'
Double Precision S_suction, T_s_comp_out, h_s_comp_out Double Precision w _isentropic, isen_ work_efficiency Double Precision w _compressor, InvertecEfficiency Double Precision C_comp4, C_comp5, C_comp6 Logical Range
C Model Final Outputs [W, 0c] q_evaporator = testoutpucmod(testnum,I)*0.OO0293 q_sensible = testoutpuCmod(testnum,3)*0.000293 q_Iatent = testoutpuCmod(testnum,4)*0.OO0293 T_airevap_out = (testoutpucmod(testnum,18)-32)*5/9 relhum_out = testoutpucmod(testnum, 50)
C Isentropic Work of Compression [kJ/kg] Call SPTInt(reCprint,(P _suction * 14.6961101.35)
* , (T_suction*9/5 + 32), S_suction, Range) Call TPSiter(reCprint, (P _condenser_in*14.6961101.35)
* , S_suction, T_s_comp_out) Call HPTInt(reCprint, (P _condenser_in * 14.696/101.35)
* , T_s_comp_out, h_s_comp_out, range) h_s_comp_out = h_s_comp_out * 2.3244 w _isentropic = h_s_comp_out - h_suction
C Compressor Isentropic Work Efficiency C_comp4 = 0.09940 C_comp5 = -0.24169 C_comp6 = 0.60555
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Isen_ Work_Efficiency = C_comp4 * P _condenser_inIP _suction * + C_comp5 * CompressocSpeed/3450 + C_comp6
C Actual Work of Compression [kJ/kg] w _compressor = w_isentropic/lsen_ Work_Efficiency
C Compressor Power [kW] Inverter_Efficiency = 0.98424*(1-exp( -5.9264*Compressor_Speed
* 13450)) Compressor_Power = mdocrefrigerant * w _compressor
* 1(0.9*InvertecEfficiency)
C Air Side Pumping Power PPair = testoutpucmod(testnum,43)
C COP Calculation COP = q_evaporator/(Compressor_Power+PPair)
Return End
EQUIVLNT.INC
C********************************************************************* C This fIle contains Equivalence statements that allow variable and C parameter names from the model to share memory locations with C elements of the XK array, thus when one is changed, the other is C automatically u1 lated. C The fIle is included anywhere the variables or parameters need to be C accessed by name or by XK#. C*********************************************************************
Double Precision XK(300) CommonIXKtogetherlXK
C ***** Counter of solver solutions integer solvercall_count Commonlcountvar/solvercall_count
C ***** Variable and parameter name declarations ***** Double Precision dT_subcool, h_expansionvalve Double Precision mdotair, mdoCrefrigerant Double Precision P _condenser_in, P _expvalve_in Double Precision P _LiqLine_in, relhum_in Double Precision T_airevap_in, Valve_Position Double Precision P _refevap_in, P _airevap_in Double Precision CompressocSpeed, h_suction Double Precision dT _superheat, P _suction, T _suction Double Precision CompressocPower, q_evaporator
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Double Precision q_sensible, q_Iatent, T_airevap_out Double Precision COP, coilnum_solver, reftype_solver Double Precision PPair, relbum_out
C *** Make XK elements equivalent to named variables *** Equivalence (XK( 1), Valve_Position) Equivalence (Xl(( 2), dT_superheat)
XK
Equivalence (XK( 3), coilnum_solver) Equivalence (XK( 4), reftype_solver) Equivalence. (XK( 5), CompressocSpeed) Equivalence (XK( 6), dT _subcool } Equivalence (XK( 7), mdotair ) Equivalence (XK( 8), T_airevap_in ) Equivalence (XK( 9), relhum_in ) Equivalence ( XK( 10), P _airevap_in) Equivalence (XK( 11), P _condensecin) Equivalence ( XK( 12), P _LiqLine_in) Equivalence ( XK( 13), P _expvalve_in ) Equivalence ( XK( 14), P _refevap_in) Equivalence (XK( 15), h_expansionvalve) Equivalence (XK( 16), P _suction) Equivalence ( XK( 17), h_suction) Equivalence ( XK( 18), T_suction) Equivalence (XK( 19), mdoCrefrigerant) Equivalence ( XK( 20), T_airevap_out) Equivalence (XK( 21), relhum_out) Equivalence (XK( 22), q_sensible) Equivalence ( XK( 23), q_Iatent) Equivalence (XK( 24), q_evaporator) Equivalence ( XK( 25), Compressor_Power) Equivalence ( XK( 26), COP) Equivalence ( XK( 27), PPair)
** XK initialization file: initializes variable guesses and parameter values. ** Output Flag specifies if variable is printed to spreadsheet readable file. ** ( 1 = Print, 0 = Don't Print) ** Parameters are flagged with "K" and variables are flagged with "X." ** The units are delimited with '[]'. ** The last number signifies the number of decimal places (0-10). ** The ORDER of the input lines CANNOT CHANGE without program modification. Output Flag Name XK# Value Units # of digit *********** DO NOT DELETE THESE FIRST NINE LINES! *************** 1 K Valve_Position = XK( 1) = 5.0000 [turns] 4 1 K dT_superheat = XK( 2) = 10.55 [deg C] 2 1 K coilnum_solver = XK( 3) = 11.0 [] 1 1 K reftype_solver = XK( 4) = 2.0 [] 1 1 K Compressor_Speed = XK( 5) = 3450.0 [RPM] 1
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1 K dT_subcool 1 K mdotair 1 K T_airevap_in 1 K relhum_in 1 K P _airevap_in 1 K P _condensecin 1 K P _LiqLine_in 1 K P _expvalve_in 1 K P Jefevap_in 1 K h_expansionvalve 1 K P _suction 1 K h_suction 1 K T _suction 1 X mdoCrefrigerant 1 K T _airevap_out 1 K relhum_out 1 K q_sensible 1 K q_Iatent 1 K q_evaporator 1 K CompressocPower 1 K COP 1 K PPair
INITMOD.f
=XK( 6) = =XK( 7) = =XK( 8) = =XK( 9) = =XK( 10) = = XK( 11) = =XK( 12) = = XK( 13) = = XK( 14) = =XK( 15) = = XK( 16) = = XK( 17) = = XK( 18) = = XK( 19) = =XK( 20) = = XK( 21) = =XK( 22) = =XK( 23) = =XK( 24) = =XK( 25) = =XK( 26) = =XK( 27) =
4.00 [deg C] 0.5500 [kg/s] 28.33 [deg C] 0.62 [] 101.35 [kPa] 1750.000 [kPa] 1646.21 [kPa] 1628.6 [kPa] 741.01 [kPa] 103.37 [kJ/kg] 685.37 [kPa] 283.58 [kJ/kg] 22.54 [deg C] 0.064444 [kg/s] 15.96 [deg C] 0.90 [] 6.8366 [kW] 6.0539 [kW] 12.9905 [kW] 3.1340 [kW] 4.1255 [] 0.0148 [kW]
2 4 2 2 2 3 2 1 2 2 2 2 2 6 2 2 4 4 4 4 4 4
C ****************************************************************** C C This fIle initializes the "RACMOD" model. C C Developed by Greg Hahn, Casey Mullen, and Kevin Porter C Modified for Split System Air Conditioner Model by Tim Nygaard C C ******************************************************************
C C
C C C C C C C
Subroutine InitializeModel(XKFilNm)
INPUTS XKFilNm
OUTPUTS X Xnm XK XKmn Xmap
- variable and parameter initialization fIlename
- variable array - variable name array - array containing both variables and parameters - array containing name of variables and parameters - Maps between X and XK
Xmap(n) = XK# of the nth variable
Implicit None
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Include 'DIMENSN.INC' Character*20 XKFilNm Character* 100 Linstr, Value Character*20 Name Character*30 Unit Character*50 Digit Character*5 .OutputStr Character* 1 ans Integer i,XKindex,Kindex,Xindex,PosEq,PosLBrack,PosRBrack,Linlen Integer NonZeroList(Xmax,O:Xmax+ 1) CommonINonZeroBlockINonZeroList
Character*3 Ans$ Logical NonZeroFlag,Already Asked CommonINZLlNonZeroFlag,Already Asked
Include 'XANDKCOM.INC' Include 'XKCOM.INC' Include 'EQUIVLNT.INC'
C *** Required for Evaporator Model Initialization *** Include 'seg.inc' Include 'hx.inc' Include 'refprop.inc'
C *** Initialize solver call counter solvercalCcount = 0
C NumVar C NumPar C i,j
- Number of variables = number of equations - Number of parameters - counters
C PosEq C LinLen C linstr C Value
- position of equals sign in a line - length of the relevant string - stores a line of Characters -stores the numeric part of a Character string
C *** Specifies the number of parameters and number of Newton-Raphson C *** variables in the model.
NumPar = 25 NumVar = 2
C This statement is needed only when REFPROP is being used C *** Initialize REFPROP thermodynamic routines *** ! Call Initial
If (AlreadyAsked) Goto 5 C *** Ask the user whether the NonZeroList should be rebuilt *** 3 Write(6,*)' Rebuild the NonZeroList?'
Write(* ,2)' "y" if residual equations have been modified or " & 'if parameters and/or'
Write(*,*)' variables have been swapped (yIn).' 2 Format (A50,A21)
Read(* ,4,err=3) Ans$ 4 Format (A3)
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AlreadyAsked = .true. If ((Ans$(l: l).eq.'y').OR.(Ans$(l: l).eq.'Y'» then
NonZeroFlag =.true. Else
NonZeroFlag = .false. Endif
C *** Read variable and parameter values and names from the fIle C *** named by XKFilnm and store them in XK and XKnm. Simultaneously C *** generate Xmap and put values in X and Xnm .
. 5 Open (unit=lO,file=XKFiINm,status='old') Xindex = 1 Kindex = 1
C *** Read the fIrst nine lines ( an informational header) *** Do i = 1,9
read(1O,*) EndDo
C ** Read and parse each line: Output, Flag, Name, Value, Unit, Digit ** Do 50 XKindex = 1, NumPar+Numvar
read( 1 O,fmt= 1 O,err= 100,End=200) Linstr 10 Format(Al00)
OutputStr = Linstr(l: 1) XKflags(XKindex) = Linstr(4:4) PosEq = INDEX(Linstr, '=') Name = Linstr(7:POSEQ-l) PosLBrack = INDEX(Linstr,'[') PosRBrack = INDEX(Linstr,'],) Value = Linstr(PosEq+ 11 :PosLBrack - 1) Unit = Linstr(PosLBrack :PosRBrack) Linlen = LEN (Linstr) . Digit = Linstr(PosRBrack + 1 :LinLen) XKnm(XKindex) = Name read(OutputStr ,21) XKOutput(XKindex) read(Value,20) XK(XKindex)
20 Format(D60.20) 21 Format(Il)
XKUnit(XKIndex) = Unit read(Digit,22) XKDigit(XKIndex)
22 Format(I40) C *** Check XKflags to see if this line contains a variable and *** C *** then make Xmap and assign the proper values to to X and Xnm***
If (XKflags(XKindex) .EQ. 'K') Then Kindex = Kindex + 1
Elself (XKflags(XKindex) .EQ. 'X') Then Xmap(Xindex) = XKindex Xnm (Xindex) = XKnm(XKindex) X(Xindex) = XK(XKIndex) Xindex = Xindex + 1
Else Write(*, *) XKflags(XKindex),
& ' is not a valid Flag in the following line:' Write(*, *) Linstr Goto 200
Endlf
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50 Continue Close(10) Goto 200
100 Write(*,*)' ERROR READING FILE:', XKFilNm Stop
C *** Check to ensure that the specified number of variables *** C *** and parameters have been given. ***
200 If ((Kindex-1 .NE. NumPar) .OR. (Xindex-1 .NE. NumVar)) Then Write(*, *) 'The number of parameters or variables is wrong!'
&
& 210
Write(*,21O) NumPar,' parameters were expected and ' ,Kindex -1,' were found.'
Write(*,21O) NumVar,' variables were expected and' ,Xindex -1,' were found.'
Format(I3,A30,I3,A12) Stop
EndIf
C *** Check NonZeroFlag to determine whether the NonZeroList can be *** C *** loaded from a file or must be rebuilt. ***
If (NonZeroFlag) Then Write(*,*) 'Creating NonZeroList.' Call CreateNonZeroList(N onZeroList) NonZeroFlag = .false.
Else Write(*, *) , Reading NonZeroList from file.' Call ReadNonZeroList(Num V ar,NonZeroList)
EndIf
Return End
SLVERSET
************************************************ ******** NEWTON-RAPHSON SETTINGS ********** Instruction file name : INSTR Step factor for partial derivatives : .0030 Maximum allowable NR iterations : 10 Convergence criteria 1 (Maximum residual) : 1.0e-5 Convergence criteria 2 (RMS residual) : 1.0e-5 Selected convergence criteria (l or 2) : 1 NR step relaxation parameter : 1.0 Use sparse matrix techniques? : .FALSE. Update guesses between runs? : .TRUE.
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******** GENERAL OUTPUT SETTINGS ********** Send general outputto screen? : .TRUE. Send general outputto a fIle? : .FALSE. Print abbreviated solver settings? : .TRUE. Print initial XK values? : .FALSE. Print initial residual vallies? : .FALSE. Print iteration summaries? : .TRUE. Print intennediate XK values? : .FALSE. Print intennediate residual values? : .FALSE. Print final XK values? : .FALSE. Print fmal residual values? : .FALSE. Print a final summary : .F ALSE .
. ******** SOLUTION OUTPUT SETTINGS ********* Save XK values in input fIle fonnat? : .TRUE. Save XK values in spreadsheet fonnat? : .TRUE. Output digits 0-10 (-1 = as in XK fIle) : -1
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